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2
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666,262,453B
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1999-12-11 03:00:00
2025-04-28 00:58:08
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A379402
Rectangular array, read by descending antidiagonals: the Type 2 runlength index array of A039701 (primes mod 3); see Comments.
[ "1", "2", "9", "3", "11", "15", "4", "16", "18", "54", "5", "21", "23", "58", "91", "6", "32", "36", "102", "110", "205", "7", "37", "39", "129", "160", "272", "194", "8", "40", "46", "161", "167", "419", "271", "139", "10", "47", "55", "174", "238", "499", "416", "260", "86", "12", "56", "73", "245", "273", "597", "496", "359", "257", "357", "13", "67", "96", "274", "292" ]
[ "nonn", "tabl" ]
14
1
2
[ "A000040", "A039701", "A379046", "A379401", "A379402", "A379403", "A379404" ]
null
Clark Kimberling, Jan 15 2025
2025-03-31T07:00:35
oeisdata/seq/A379/A379402.seq
98b61c871001e28d538605de9cee0635
A379403
Rectangular array, read by descending antidiagonals: the Type 1 runlength index array of A039702 (primes mod 4); see Comments.
[ "1", "2", "5", "3", "7", "20", "4", "9", "26", "23", "6", "13", "39", "71", "48", "8", "15", "60", "93", "80", "49", "10", "25", "76", "137", "94", "89", "96", "11", "28", "79", "156", "140", "95", "204", "133", "12", "30", "92", "187", "157", "199", "241", "356", "242", "14", "32", "113", "230", "198", "236", "271", "512", "457", "243", "16", "45", "118", "260", "233", "268" ]
[ "tabl", "nonn" ]
12
1
2
[ "A039702", "A379046", "A379401", "A379402", "A379403", "A379404" ]
null
Clark Kimberling, Jan 15 2025.
2025-03-31T07:00:39
oeisdata/seq/A379/A379403.seq
8b250ff42a30dfd68e721f7a24924e10
A379404
Rectangular array, by descending antidiagonals: the Type 2 runlength index array of A039702 (primes mod 4); see Comments.
[ "1", "2", "4", "3", "6", "19", "5", "8", "24", "46", "7", "12", "47", "78", "31", "9", "22", "65", "128", "77", "14", "10", "25", "72", "135", "93", "50", "91", "11", "27", "87", "154", "134", "92", "168", "239", "13", "29", "94", "197", "153", "183", "240", "337", "232", "15", "38", "97", "247", "196", "241", "400", "540", "254", "229", "16", "44", "114", "264", "246", "435" ]
[ "nonn", "tabl" ]
10
1
2
[ "A039702", "A379046", "A379401", "A379402", "A379403", "A379404" ]
null
Clark Kimberling, Jan 15 2025
2025-03-31T07:00:43
oeisdata/seq/A379/A379404.seq
c88b0524ce455c2ad5cd20f42e528f02
A379405
a(n) = p((n+1)*p(n)), where p(x) = least prime > x; i.e., p = A151800.
[ "3", "5", "11", "23", "29", "43", "53", "89", "101", "113", "127", "157", "173", "239", "257", "277", "293", "347", "367", "461", "487", "509", "541", "701", "727", "757", "787", "821", "853", "937", "967", "1187", "1223", "1259", "1297", "1361", "1373", "1559", "1601", "1657", "1693", "1811", "1861", "2069", "2129", "2179", "2213", "2549", "2609", "2657" ]
[ "nonn" ]
23
0
1
[ "A000040", "A053024", "A151800", "A378135", "A378136", "A378137", "A379405" ]
null
Clark Kimberling, Jan 18 2025
2025-01-21T18:20:14
oeisdata/seq/A379/A379405.seq
a02ce724db53629e4e1585bc93ca7956
A379406
a(n) = A379511(n) - A378142(n).
[ "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "0", "1", "1", "1", "0", "0", "0", "1", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "1", "1", "1", "1", "0", "0", "1", "1", "1", "1", "0", "0", "1", "1", "1", "0", "0" ]
[ "nonn" ]
4
1
null
[ "A378142", "A379406", "A379511" ]
null
Clark Kimberling, Jan 18 2025
2025-01-20T17:10:29
oeisdata/seq/A379/A379406.seq
bad9786f232e4e5709b44f7f8a496626
A379407
a(n) is the smallest semiprime > primorial(n).
[ "4", "9", "33", "213", "2315", "30031", "510515", "9699691", "223092871", "6469693233", "200560490134", "7420738134814", "304250263527221", "13082761331670031", "614889782588491414", "32589158477190044737", "1922760350154212639074", "117288381359406970983271", "7858321551080267055879091" ]
[ "nonn" ]
13
1
1
[ "A001358", "A002110", "A089539", "A106325", "A379407" ]
null
Alexandre Herrera, Dec 22 2024
2025-01-12T21:05:59
oeisdata/seq/A379/A379407.seq
6434202c4708526846816007372d8110
A379408
a(n) = n + floor(n*s/r) + floor(n*t/r), where r = u^(1/4); s = u^(1/2); t = u^(3/4), u = golden ratio (A001622).
[ "3", "6", "9", "13", "16", "19", "22", "27", "30", "33", "36", "40", "43", "46", "50", "54", "57", "60", "64", "67", "70", "73", "77", "81", "84", "88", "91", "94", "97", "101", "104", "108", "111", "115", "118", "121", "125", "128", "131", "135", "139", "142", "145", "148", "152", "155", "159", "163", "166", "169", "172", "176", "179", "182", "186", "190", "193", "196" ]
[ "nonn" ]
10
1
1
[ "A000027", "A001622", "A379408", "A379409", "A379410" ]
null
Clark Kimberling, Jan 15 2025
2025-01-18T09:25:06
oeisdata/seq/A379/A379408.seq
3d4c0fd62ae2d14fbd72a84a4d4979e4
A379409
a(n) = n + floor(n*r/s) + floor(n*t/s), where r = u^(1/4); s = u^(1/2); t = u^(3/4), u = golden ratio (A001622).
[ "2", "5", "8", "11", "14", "17", "20", "24", "26", "29", "32", "35", "38", "41", "44", "48", "51", "53", "56", "59", "62", "65", "68", "72", "75", "78", "80", "83", "86", "89", "92", "96", "99", "102", "105", "107", "110", "113", "116", "120", "123", "126", "129", "132", "134", "137", "141", "144", "147", "150", "153", "156", "158", "161", "165", "168", "171", "174", "177" ]
[ "nonn" ]
8
1
1
[ "A001622", "A379408", "A379409", "A379410" ]
null
Clark Kimberling, Jan 15 2025
2025-01-18T09:25:37
oeisdata/seq/A379/A379409.seq
322dd703df62c5e055445955cd84cf1a
A379410
a(n) = n + floor(n*r/t) + floor(n*s/t), where r = u^(1/4), s = u^(1/2), t = u^(3/4), u = golden ratio (A001622).
[ "1", "4", "7", "10", "12", "15", "18", "21", "23", "25", "28", "31", "34", "37", "39", "42", "45", "47", "49", "52", "55", "58", "61", "63", "66", "69", "71", "74", "76", "79", "82", "85", "87", "90", "93", "95", "98", "100", "103", "106", "109", "112", "114", "117", "119", "122", "124", "127", "130", "133", "136", "138", "140", "143", "146", "149", "151", "154", "157", "160", "162", "164", "167", "170" ]
[ "nonn" ]
14
1
2
[ "A001622", "A184908", "A379408", "A379409", "A379410" ]
null
Clark Kimberling, Jan 21 2025
2025-01-28T10:41:35
oeisdata/seq/A379/A379410.seq
350c5189eb4b7ee3ed213c6f5c92b9a6
A379411
a(n) = n + floor(n*s/r) + floor(n*t/r), where r = e^(1/4), s = e^(1/2), t = e^(3/4).
[ "3", "7", "10", "15", "19", "22", "26", "31", "34", "38", "43", "46", "50", "54", "58", "62", "66", "70", "74", "77", "81", "86", "89", "93", "98", "101", "105", "109", "113", "117", "121", "125", "129", "133", "136", "141", "145", "148", "153", "156", "160", "164", "168", "172", "176", "180", "184", "188", "191", "196", "200", "203", "208", "212", "215", "219", "223" ]
[ "nonn" ]
10
1
1
[ "A019774", "A092042", "A184812", "A331501", "A379411", "A379412", "A379413" ]
null
Clark Kimberling, Jan 18 2025
2025-01-20T17:10:50
oeisdata/seq/A379/A379411.seq
668ecc73087fa5adf1d4b7d505092ff7
A379412
a(n) = n + floor(n*r/s) + floor(n*t/s), where r = e^(1/4); s = e^(1/2); t = e^(3/4).
[ "2", "5", "8", "12", "14", "17", "20", "24", "27", "29", "33", "36", "39", "41", "45", "48", "51", "55", "57", "60", "63", "67", "69", "72", "76", "79", "82", "84", "88", "91", "94", "97", "100", "103", "106", "110", "112", "115", "119", "122", "124", "127", "131", "134", "137", "140", "143", "146", "149", "152", "155", "158", "162", "165", "167", "170", "174", "177", "179" ]
[ "nonn" ]
8
1
1
[ "A001113", "A378142", "A379411", "A379412", "A379413" ]
null
Clark Kimberling, Jan 15 2025
2025-01-18T09:26:05
oeisdata/seq/A379/A379412.seq
45be46be462488f7d7d1a768ea2c42f8
A379413
a(n) = n + floor(n*r/t) + floor(n*s/t), where r = e^(1/4), s = e^(1/2), t = e^(3/4).
[ "1", "4", "6", "9", "11", "13", "16", "18", "21", "23", "25", "28", "30", "32", "35", "37", "40", "42", "44", "47", "49", "52", "53", "56", "59", "61", "64", "65", "68", "71", "73", "75", "78", "80", "83", "85", "87", "90", "92", "95", "96", "99", "102", "104", "107", "108", "111", "114", "116", "118", "120", "123", "126", "128", "130", "132", "135", "138", "139", "142", "144" ]
[ "nonn" ]
8
1
2
[ "A019774", "A092042", "A331501", "A378142", "A379411", "A379412", "A379413" ]
null
Clark Kimberling, Jan 18 2025
2025-01-20T17:11:16
oeisdata/seq/A379/A379413.seq
2c9668d17e951eb4e6529b3852472f09
A379414
a(n) = n + floor(n*s/r) + floor(n*t/r), where r = 3^(1/4), s = 3^(1/2), t = 3^(3/4).
[ "3", "7", "11", "15", "19", "23", "28", "31", "35", "40", "44", "47", "52", "56", "59", "64", "68", "72", "76", "80", "84", "88", "92", "96", "100", "105", "108", "112", "117", "120", "124", "129", "133", "136", "141", "145", "149", "153", "157", "161", "165", "169", "173", "177", "181", "185", "189", "194", "197", "201", "206", "210", "213", "218", "222", "225", "230" ]
[ "nonn" ]
9
1
1
[ "A002194", "A011002", "A011022", "A184812", "A379414", "A379415", "A379416" ]
null
Clark Kimberling, Jan 18 2025
2025-01-20T17:11:59
oeisdata/seq/A379/A379414.seq
bb60af2266873733903e8e8dce2352bf
A379415
a(n) = n + floor(n*r/s) + floor(n*t/s), where r = 3^(1/4), s = 3^(1/2), t = 3^(3/4).
[ "2", "5", "8", "12", "14", "17", "21", "24", "26", "30", "33", "36", "39", "42", "45", "49", "51", "54", "58", "61", "63", "66", "70", "73", "75", "79", "82", "85", "89", "91", "94", "98", "101", "103", "107", "110", "113", "116", "119", "122", "125", "128", "131", "134", "138", "140", "143", "147", "150", "152", "156", "159", "162", "166", "168", "171", "175", "178", "180" ]
[ "nonn" ]
9
1
1
[ "A002194", "A011002", "A011022", "A184812", "A379415", "A379416" ]
null
Clark Kimberling, Jan 18 2025
2025-01-20T17:12:34
oeisdata/seq/A379/A379415.seq
81284be4c38fb1b561cc85fd8a381e07
A379416
a(n) = n + [n*r/t] + [n*s/t], where r = 3^(1/4); s = 3^(1/2); t = 3^(3/4) and [ ] = floor.
[ "1", "4", "6", "9", "10", "13", "16", "18", "20", "22", "25", "27", "29", "32", "34", "37", "38", "41", "43", "46", "48", "50", "53", "55", "57", "60", "62", "65", "67", "69", "71", "74", "77", "78", "81", "83", "86", "87", "90", "93", "95", "97", "99", "102", "104", "106", "109", "111", "114", "115", "118", "121", "123", "126", "127", "130", "132", "135", "137", "139", "142" ]
[ "nonn" ]
4
1
2
[ "A184812", "A379414", "A379415", "A379416" ]
null
Clark Kimberling, Jan 20 2025
2025-01-20T22:46:04
oeisdata/seq/A379/A379416.seq
d40f6f992e95624d2e52ee965e3dbd46
A379417
a(n) = n + [n*s/r] + [n*t/r], where r = (3/2)^(1/4); s = (3/2)^(1/2); t = (3/2)^(3/4) and [ ] = floor.
[ "3", "6", "9", "12", "16", "19", "22", "25", "29", "33", "36", "39", "42", "46", "49", "52", "55", "59", "63", "66", "69", "72", "76", "79", "82", "85", "89", "92", "96", "99", "102", "106", "109", "112", "115", "119", "122", "126", "129", "132", "136", "139", "142", "145", "149", "152", "156", "159", "163", "166", "169", "172", "175", "179", "182", "185", "189", "193" ]
[ "nonn" ]
4
1
1
[ "A184812", "A379417", "A379418", "A379419" ]
null
Clark Kimberling, Jan 20 2025
2025-01-20T22:46:13
oeisdata/seq/A379/A379417.seq
3da1c3447031d8cff2440379544f9cf6
A379418
a(n) = n + [n*r/s] + [n*t/s], where r = (3/2)^(1/4); s = (3/2)^(1/2); t = (3/2)^(3/4) and [ ] = floor.
[ "2", "5", "8", "11", "14", "17", "20", "23", "26", "30", "32", "35", "38", "41", "44", "47", "50", "53", "57", "60", "62", "65", "68", "71", "74", "77", "80", "83", "87", "90", "93", "95", "98", "101", "104", "107", "110", "114", "117", "120", "123", "125", "128", "131", "134", "137", "141", "144", "147", "150", "153", "155", "158", "161", "164", "167", "171", "174", "177" ]
[ "nonn" ]
4
1
1
[ "A184812", "A379417", "A379418", "A379419" ]
null
Clark Kimberling, Jan 20 2025
2025-01-20T22:46:21
oeisdata/seq/A379/A379418.seq
860b08ed8e8c703c099b9edcb76152a1
A379419
a(n) = n + [n*r/t] + [n*s/t], where r = (3/2)^(1/4); s = (3/2)^(1/2); t = (3/2)^(3/4) and [ ] = floor.
[ "1", "4", "7", "10", "13", "15", "18", "21", "24", "27", "28", "31", "34", "37", "40", "43", "45", "48", "51", "54", "56", "58", "61", "64", "67", "70", "73", "75", "78", "81", "84", "86", "88", "91", "94", "97", "100", "103", "105", "108", "111", "113", "116", "118", "121", "124", "127", "130", "133", "135", "138", "140", "143", "146", "148", "151", "154", "157", "160" ]
[ "nonn" ]
4
1
2
[ "A184812", "A379417", "A379418", "A379419" ]
null
Clark Kimberling, Jan 20 2025
2025-01-20T22:46:28
oeisdata/seq/A379/A379419.seq
9a51f61c4af275e188c521e671d8ba22
A379420
a(n) = n + [n*s/r] + [n*t/r], where r = 5^(1/4); s = 5^(1/2); t = 5^(3/4) and [ ] = floor.
[ "4", "8", "13", "17", "23", "27", "32", "36", "42", "46", "51", "55", "61", "65", "70", "74", "80", "84", "89", "93", "98", "103", "108", "112", "117", "122", "127", "131", "136", "141", "146", "150", "155", "160", "165", "169", "174", "178", "184", "188", "193", "197", "203", "207", "212", "216", "222", "226", "231", "235", "241", "245", "250", "254", "259", "264" ]
[ "nonn" ]
5
1
1
[ "A184812", "A379420", "A379421", "A379422" ]
null
Clark Kimberling, Jan 20 2025
2025-01-20T22:46:35
oeisdata/seq/A379/A379420.seq
ae2be5ed3b94aaa160a01f1e7043fa4f
A379421
a(n) = n + floor(n*r/s) + floor(n*t/s), where r = 5^(1/4), s = 5^(1/2), t = 5^(3/4).
[ "2", "5", "9", "11", "15", "18", "21", "24", "28", "30", "34", "37", "40", "43", "47", "49", "53", "56", "59", "62", "66", "68", "72", "75", "78", "81", "85", "87", "91", "94", "97", "100", "104", "106", "110", "113", "116", "119", "123", "125", "129", "132", "135", "138", "142", "144", "148", "151", "154", "157", "161", "163", "167", "170", "173", "176", "180", "182" ]
[ "nonn" ]
6
1
1
[ "A184812", "A379420", "A379421", "A379422" ]
null
Clark Kimberling, Jan 21 2025
2025-01-26T20:59:41
oeisdata/seq/A379/A379421.seq
bda6a743aa90e60d6f003c4f5467b701
A379422
a(n) = n + floor(n*r/t) + floor(n*s/t), where r = 5^(1/4), s = 5^(1/2), t = 5^(3/4).
[ "1", "3", "6", "7", "10", "12", "14", "16", "19", "20", "22", "25", "26", "29", "31", "33", "35", "38", "39", "41", "44", "45", "48", "50", "52", "54", "57", "58", "60", "63", "64", "67", "69", "71", "73", "76", "77", "79", "82", "83", "86", "88", "90", "92", "95", "96", "99", "101", "102", "105", "107", "109", "111", "114", "115", "118", "120", "121", "124", "126", "128", "130" ]
[ "nonn" ]
7
1
2
[ "A184812", "A379420", "A379421", "A379422" ]
null
Clark Kimberling, Jan 21 2025
2025-01-26T20:59:49
oeisdata/seq/A379/A379422.seq
4b59aba28fc72b0051cb6b48e656554c
A379423
Least modulus k such that the multiplicative group modulo k is the direct product of n nontrivial cyclic groups.
[ "1", "3", "7", "21", "56", "168", "504", "1736", "5208", "15624", "57288", "171864", "671832", "2234232", "7390152", "32023992", "96071976", "450799272", "1559322072", "5860390536", "20271186936", "95118646392", "385152551784", "1236542403096", "6182712015480", "23494305658824", "82848341007432", "409295535424776" ]
[ "nonn" ]
24
0
2
[ "A102476", "A379423" ]
null
Asher Gray, Dec 22 2024
2025-01-20T00:47:39
oeisdata/seq/A379/A379423.seq
cdb06d2359487b497239600cd47da230
A379424
Least modulus k such that the multiplicative group modulo k has a difference of n nontrivial cycles between its minimal and maximal representation.
[ "1", "7", "31", "211", "1333", "6541", "45787", "281263", "1968841", "13781887", "93098053", "649998793", "4549991551", "31849940857", "215149600483", "1506047203381", "10542330423667", "86982188480467", "587573558919073", "4113014912433511", "28791104387034577", "247368468304929733" ]
[ "nonn" ]
20
0
2
[ "A102476", "A379423", "A379424" ]
null
Asher Gray, Dec 22 2024
2025-01-20T00:47:47
oeisdata/seq/A379/A379424.seq
2fee84785507324ff77bf8d2a90987d5
A379425
Decimal expansion of Ni_2 = gamma/3 - log(2*Pi)/2 - 2*zeta'(-1) + 2/3, where gamma = A001620.
[ "2", "7", "0", "9", "7", "5", "6", "4", "2", "4", "9", "6", "7", "4", "0", "0", "7", "0", "1", "8", "3", "0", "1", "3", "6", "1", "4", "1", "0", "7", "4", "1", "1", "1", "2", "2", "6", "8", "0", "7", "2", "8", "3", "9", "9", "0", "1", "2", "5", "9", "4", "6", "8", "7", "4", "5", "1", "1", "4", "8", "8", "1", "7", "1", "9", "3", "5", "7", "6", "2", "7", "8", "9", "9", "8", "4", "4", "8", "8", "3", "8", "1", "3", "6", "6", "2", "2", "5", "8", "9", "7", "9", "2", "9", "7", "8", "8", "9", "6", "6", "2", "6", "2", "9", "2" ]
[ "cons", "nonn" ]
21
0
1
[ "A000796", "A001620", "A074962", "A131688", "A321943", "A379425", "A379751" ]
null
Artur Jasinski, Dec 22 2024
2025-01-03T02:00:51
oeisdata/seq/A379/A379425.seq
cdf5141c458780289a5f90cb77d41c98
A379426
Prime terms in A287353.
[ "2", "23", "2357", "23581", "2358247", "235824913", "235824916247", "2358249162515829584909", "235824916251582958491829824917162558516292249258249589629182571583855789", "2358249162515829584918298249171625585162922492582495896291825715838558298516316558918298250261" ]
[ "nonn" ]
4
1
1
[ "A013918", "A069151", "A287353", "A379426" ]
null
Ya-Ping Lu, Dec 22 2024
2024-12-23T01:56:11
oeisdata/seq/A379/A379426.seq
8a495d1c5446ffda77b920bcff31ae0e
A379427
Numbers n such that prime(k)*n+prime(k+1), for k=1,...,8 all are primes.
[ "5600384", "12269234", "12700154", "37311314", "53311754", "89357594", "102873404", "149030894", "195567434", "198261194", "329024954", "415090604", "446799044", "518371124", "548711084", "718560344", "832935284", "974972324", "980770004", "1006398854", "1053870704", "1081009334", "1084372994", "1119125894" ]
[ "nonn" ]
4
1
1
[ "A108110", "A108117", "A379427" ]
null
Jason Yuen, Dec 22 2024
2024-12-23T01:53:16
oeisdata/seq/A379/A379427.seq
316534a4fc6bc2852f665159485d6464
A379428
Numbers k such that (39^k + 2^k)/41 is prime.
[ "3", "5", "19", "2543", "4691", "14669", "19819", "53891", "83137" ]
[ "nonn", "hard", "more" ]
5
1
1
[ "A057187", "A057188", "A062587", "A062589", "A127996", "A127997", "A128344", "A204940", "A217320", "A225807", "A228922", "A229542", "A375161", "A375236", "A377031", "A377856", "A379428" ]
null
Robert Price, Dec 22 2024
2025-02-16T08:34:07
oeisdata/seq/A379/A379428.seq
27b679ebbee82db1ea94635612c4fda4
A379429
Numbers k such that (31^k + 2^k)/33 is prime.
[ "229", "1429", "36083", "44089" ]
[ "nonn", "hard", "more" ]
5
1
1
[ "A057187", "A057188", "A062587", "A062589", "A127996", "A127997", "A128344", "A204940", "A217320", "A225807", "A228922", "A229542", "A375161", "A375236", "A377031", "A377856", "A379429" ]
null
Robert Price, Dec 22 2024
2025-02-16T08:34:07
oeisdata/seq/A379/A379429.seq
ee971105c463e5501735c5543a968069
A379430
Array read by antidiagonals: A(n,k) is the number of sensed planar maps with n vertices and k faces, n >= 1, k >= 1.
[ "1", "1", "1", "1", "2", "1", "2", "5", "5", "2", "3", "14", "23", "14", "3", "6", "42", "108", "108", "42", "6", "14", "140", "501", "761", "501", "140", "14", "34", "473", "2264", "4744", "4744", "2264", "473", "34", "95", "1670", "10087", "27768", "38495", "27768", "10087", "1670", "95", "280", "5969", "44310", "153668", "279698", "279698", "153668", "44310", "5969", "280" ]
[ "nonn", "tabl" ]
10
1
5
[ "A002995", "A006384", "A269920", "A277741", "A342061", "A379430", "A379431" ]
null
Andrew Howroyd, Jan 13 2025
2025-01-14T17:15:52
oeisdata/seq/A379/A379430.seq
91d397f01c198af0546d3a575e804add
A379431
Array read by antidiagonals: A(n,k) is the number of achiral planar maps with n vertices and k faces, n >= 1, k >= 1.
[ "1", "1", "1", "1", "2", "1", "2", "5", "5", "2", "3", "12", "17", "12", "3", "6", "28", "58", "58", "28", "6", "10", "68", "179", "247", "179", "68", "10", "20", "157", "538", "942", "942", "538", "157", "20", "35", "372", "1531", "3388", "4345", "3388", "1531", "372", "35", "70", "845", "4288", "11424", "18316", "18316", "11424", "4288", "845", "70" ]
[ "nonn", "tabl" ]
8
1
5
[ "A006443", "A210736", "A269920", "A277741", "A379430", "A379431" ]
null
Andrew Howroyd, Jan 14 2025
2025-01-14T17:15:45
oeisdata/seq/A379/A379431.seq
e8157ed4e6f6c010c28ed47d17373655
A379432
Triangle read by rows: T(n,k) is the number of unsensed 2-connected (nonseparable) planar maps with n edges and k vertices, n >= 2, 2 <= k <= n.
[ "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "3", "7", "3", "1", "1", "4", "13", "13", "4", "1", "1", "5", "29", "44", "29", "5", "1", "1", "7", "51", "139", "139", "51", "7", "1", "1", "8", "92", "370", "623", "370", "92", "8", "1", "1", "10", "147", "913", "2307", "2307", "913", "147", "10", "1", "1", "12", "240", "2048", "7644", "11673", "7644", "2048", "240", "12", "1", "1", "14", "357", "4295", "22344", "50174", "50174", "22344", "4295", "357", "14", "1" ]
[ "nonn", "tabl" ]
5
2
8
[ "A006403", "A082680", "A212438", "A277741", "A342060", "A342061", "A379432" ]
null
Andrew Howroyd, Jan 14 2025
2025-01-14T19:14:04
oeisdata/seq/A379/A379432.seq
e3ad1b89a6c762f49474c9fded28f7c3
A379433
Number of rooted planar maps with n edges and without faces of degree 1.
[ "1", "1", "3", "16", "96", "624", "4304", "31056", "232128", "1784752", "14043312", "112648848", "918456608", "7593649392", "63546379152", "537427956688", "4587713701248", "39488179213872", "342414691125104", "2989022121125136", "26249475365186016", "231786459869636464", "2056950693208881744" ]
[ "nonn" ]
12
0
3
[ "A000168", "A006388", "A006389", "A379433", "A379434", "A379435" ]
null
Andrew Howroyd, Jan 14 2025
2025-01-17T02:33:22
oeisdata/seq/A379/A379433.seq
8961e892cf65d07656a3bc48e99afab2
A379434
Number of rooted planar maps with n edges and without faces of degree 1 or 2.
[ "1", "0", "2", "9", "47", "278", "1720", "11175", "75149", "519852" ]
[ "nonn", "more" ]
6
0
3
[ "A000168", "A006392", "A006393", "A379433", "A379434" ]
null
Andrew Howroyd, Jan 14 2025
2025-01-16T11:30:29
oeisdata/seq/A379/A379434.seq
76da1e68edd5b482ea4764a6c29a1fc0
A379435
Number of rooted planar maps with n edges and without faces or vertices of degree 1.
[ "1", "0", "1", "2", "10", "52", "281", "1570", "9022", "53084", "318634", "1945396", "12052532", "75624616", "479814937", "3074251682", "19869323638", "129420288076", "848897059790", "5603350613308", "37198680816844", "248241480270680", "1664546969372554", "11210468046615412", "75806810042727980", "514537522249147672" ]
[ "nonn" ]
9
0
4
[ "A000168", "A006396", "A006397", "A379433", "A379435" ]
null
Andrew Howroyd, Jan 14 2025
2025-01-17T02:33:40
oeisdata/seq/A379/A379435.seq
2c7dc5b80681ecb4ff491286ddc94303
A379436
Number of rooted simple planar maps without vertices of degree 1.
[ "1", "0", "0", "1", "1", "6", "22", "92", "395", "1753" ]
[ "nonn", "more" ]
7
0
6
[ "A006400", "A006401", "A022558", "A379433", "A379436" ]
null
Andrew Howroyd, Jan 14 2025
2025-01-16T11:30:33
oeisdata/seq/A379/A379436.seq
8ba08373161892c14463f1d31d758b85
A379437
Number of rooted 2-connected simple planar maps with n edges.
[ "1", "1", "6", "16", "71", "267", "1162" ]
[ "nonn", "more" ]
7
3
3
[ "A000139", "A000168", "A006406", "A006407", "A379437" ]
null
Andrew Howroyd, Jan 16 2025
2025-01-17T02:33:52
oeisdata/seq/A379/A379437.seq
7cefc7e5ed4e3b1410c2906e8b1d2c8a
A379438
Triangle read by rows: T(n,k) is the number of sensed combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).
[ "1", "2", "4", "1", "14", "6", "57", "46", "4", "312", "452", "106", "2071", "4852", "2382", "131", "15030", "52972", "46680", "8158", "117735", "587047", "830848", "313611", "14118", "967850", "6550808", "13804864", "9326858", "1369446", "8268816", "73483256", "218353000", "236095958", "74803564", "2976853", "72833730", "827801468", "3328822880", "5345316004", "3023693380", "391288854" ]
[ "nonn", "tabf" ]
15
0
2
[ "A006384", "A006386", "A104595", "A104596", "A170946", "A215019", "A239918", "A239919", "A239921", "A239922", "A239923", "A239924", "A269919", "A379438", "A379439", "A380234", "A380235" ]
null
Andrew Howroyd, Jan 16 2025
2025-01-20T19:14:13
oeisdata/seq/A379/A379438.seq
8fac31592d1063fde18aa71a5e5ade93
A379439
Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).
[ "1", "2", "4", "1", "14", "6", "52", "40", "4", "248", "320", "76", "1416", "2946", "1395", "82", "9172", "29364", "24950", "4348", "66366", "309558", "427336", "160050", "7258", "518868", "3365108", "6987100", "4696504", "688976", "4301350", "37246245", "109761827", "118353618", "37466297", "1491629", "37230364", "416751008", "1668376886", "2675297588", "1512650776", "195728778" ]
[ "nonn", "tabf" ]
13
0
2
[ "A006385", "A006387", "A214814", "A214815", "A214816", "A269919", "A297880", "A297881", "A348798", "A348800", "A348801", "A379438", "A379439", "A380234", "A380235" ]
null
Andrew Howroyd, Jan 16 2025
2025-01-20T20:24:15
oeisdata/seq/A379/A379439.seq
9356ece6bd5726887a95b02cb98568f4
A379440
a(1) = 1, a(2) = 2, for a(n) > 2, a(n) is the smallest unused positive number that shares a factor with a(n-1) such that the exponents of each distinct prime factor of a(n) differ by one from those of the same prime factors of a(n-1).
[ "1", "2", "4", "6", "9", "3", "18", "12", "8", "16", "24", "20", "14", "44", "10", "25", "5", "50", "15", "63", "27", "45", "21", "49", "7", "98", "28", "22", "52", "30", "36", "26", "60", "34", "76", "40", "48", "32", "64", "96", "80", "56", "68", "38", "84", "46", "116", "42", "92", "58", "124", "66", "117", "33", "90", "39", "99", "51", "126", "57", "153", "54", "81", "135", "162", "108", "62", "132", "70", "75", "35", "147", "77", "121", "11", "242", "55", "150", "65", "169", "13", "338", "91", "245", "119", "289", "17" ]
[ "nonn", "look" ]
13
1
2
[ "A027746", "A051903", "A064413", "A124010", "A348086", "A379248", "A379440", "A379441", "A379442" ]
null
Scott R. Shannon, Dec 23 2024
2025-02-10T09:32:57
oeisdata/seq/A379/A379440.seq
f9815e171fa30355503171ddc9da82a8
A379441
a(1) = 1, a(2) = 2, for a(n) > 2, a(n) is the smallest unused positive number that shares a factor with a(n-1) such that the exponents of each distinct prime factor of a(n-1) differ by one from those of the same prime factors of a(n).
[ "1", "2", "4", "6", "9", "3", "18", "12", "8", "16", "24", "20", "14", "36", "30", "25", "5", "50", "15", "63", "27", "45", "21", "49", "7", "98", "28", "10", "44", "26", "60", "22", "52", "34", "76", "40", "48", "32", "64", "96", "80", "56", "68", "38", "84", "46", "100", "70", "75", "35", "147", "77", "121", "11", "242", "33", "72", "108", "90", "39", "99", "42", "92", "54", "81", "135", "117", "51", "126", "57", "144", "120", "112", "88", "116", "62", "132", "58", "124", "66", "140", "74", "156", "82", "148", "78", "153", "69" ]
[ "nonn" ]
10
1
2
[ "A027746", "A051903", "A064413", "A124010", "A348086", "A379248", "A379440", "A379441", "A379442" ]
null
Scott R. Shannon, Dec 23 2024
2025-02-10T09:32:53
oeisdata/seq/A379/A379441.seq
696cb669329ab17321159f142a6f0649
A379442
a(1) = 1, a(2) = 2, for a(n) > 2, a(n) is the smallest unused positive number that shares a factor with a(n-1) such that the exponents of each distinct prime factor of a(n-1) differ by one from those of the same prime factors of a(n), while the exponents of each distinct prime factor of a(n) differ by one from those of the same prime factors of a(n-1).
[ "1", "2", "4", "6", "9", "3", "18", "12", "8", "16", "24", "20", "14", "44", "10", "25", "5", "50", "15", "63", "27", "45", "21", "49", "7", "98", "28", "22", "52", "30", "36", "42", "68", "26", "60", "34", "76", "40", "48", "32", "64", "96", "80", "56", "92", "38", "84", "46", "116", "62", "132", "58", "124", "66", "117", "33", "90", "39", "99", "51", "126", "57", "153", "54", "81", "135", "162", "108", "72", "156", "70", "75", "35", "147", "77", "121", "11", "242", "55", "150", "65", "169", "13", "338", "91", "245", "119", "289" ]
[ "nonn" ]
17
1
2
[ "A027746", "A051903", "A064413", "A124010", "A348086", "A379248", "A379440", "A379441", "A379442", "A379557", "A379558", "A379559" ]
null
Scott R. Shannon, Dec 23 2024
2025-01-05T10:24:13
oeisdata/seq/A379/A379442.seq
1fd74f5f95a321aed29c0e1e066c71b1
A379443
Decimal expansion of the smallest positive root of the Cosine Integral function.
[ "6", "1", "6", "5", "0", "5", "4", "8", "5", "6", "2", "0", "7", "1", "6", "2", "3", "3", "7", "9", "7", "1", "1", "0", "4", "0", "4", "1", "0", "0", "1", "7", "2", "7", "4", "7", "5", "3", "9", "4", "9", "5", "8", "9", "8", "1", "8", "1", "6", "6", "5", "3", "3", "0", "5", "7", "2", "1", "2", "0", "7", "2", "1", "1", "2", "4", "7", "5", "3", "1", "5", "9", "7", "7", "4", "9", "5", "4", "0", "3", "3", "9", "5", "6", "1", "6", "4", "5", "6", "1", "6", "9", "0", "3", "4", "0", "3", "0", "1", "2", "5", "0", "3", "4", "1" ]
[ "nonn", "cons" ]
34
0
1
[ "A133746", "A379443" ]
null
Stefano Spezia, Jan 04 2025
2025-01-04T23:22:07
oeisdata/seq/A379/A379443.seq
be2316a5d354bd740724a135e0e12e40
A379444
a(n) is the difference between the least prime > (n+1)^2 and the largest prime < n^2, divided by 2.
[ "4", "5", "8", "7", "11", "10", "11", "11", "15", "18", "17", "15", "17", "17", "21", "24", "25", "21", "23", "24", "31", "27", "30", "29", "30", "30", "40", "34", "40", "39", "35", "38", "38", "37", "41", "40", "42", "45", "48", "54", "51", "51", "47", "56", "50", "51", "57", "52", "66", "57", "60", "57", "64", "57", "65", "71", "65", "69", "67", "64", "78", "66", "68", "69", "72", "77", "81" ]
[ "nonn", "easy" ]
13
2
1
[ "A001223", "A007491", "A053001", "A058043", "A350100", "A378904", "A379444" ]
null
Hugo Pfoertner, Dec 23 2024
2025-01-24T18:30:58
oeisdata/seq/A379/A379444.seq
3874c5268641200e8a9c3b1d0fcd3bfa
A379445
a(n) = gpf(prime(n)-1)*gpf(prime(n)+1), where gpf is A006530.
[ "4", "6", "6", "15", "21", "6", "15", "33", "35", "10", "57", "35", "77", "69", "39", "145", "155", "187", "21", "111", "65", "287", "55", "21", "85", "221", "159", "33", "133", "14", "143", "391", "161", "185", "95", "1027", "123", "581", "1247", "445", "65", "57", "291", "77", "55", "371", "259", "2147", "437", "377", "85", "55", "35", "86", "1441", "335", "85", "3197", "329", "3337" ]
[ "nonn" ]
23
2
1
[ "A000215", "A000668", "A006530", "A006881", "A023503", "A023509", "A058383", "A087713", "A268640", "A379445" ]
null
Hugo Pfoertner, Dec 28 2024
2025-01-22T09:57:28
oeisdata/seq/A379/A379445.seq
23e3eb73b73d880a3e1c7118093a3570
A379446
a(n) is the number of ones in the binary expansion of 10^(10^n).
[ "2", "11", "105", "1163", "11683", "115979", "1161413", "11606847", "116093517", "1160951533", "11609679812", "116096181467", "1160963225086" ]
[ "nonn", "base", "more" ]
16
0
1
[ "A000120", "A011557", "A118738", "A153201", "A379446", "A379448" ]
null
Hugo Pfoertner, Dec 26 2024
2024-12-28T09:30:51
oeisdata/seq/A379/A379446.seq
0d56be008ef84087267996f69e5083d9
A379447
a(n) is the number of ones in the binary expansion of (n^n)^n.
[ "1", "1", "8", "1", "19", "27", "68", "1", "128", "105", "209", "120", "320", "266", "442", "1", "584", "524", "774", "476", "1006", "833", "1188", "477", "1486", "1248", "1746", "1066", "2068", "1733", "2365", "1", "2735", "2328", "3134", "1982", "3598", "3085", "4062", "1823", "4415", "3937", "5038", "3309", "5571", "4808", "6137", "1790", "6794", "5768", "7381" ]
[ "nonn", "base" ]
6
1
3
[ "A000120", "A002489", "A379447", "A379448" ]
null
Hugo Pfoertner, Dec 26 2024
2024-12-26T12:34:56
oeisdata/seq/A379/A379447.seq
f1ab8133ae0ee68c4dee9ec189047982
A379448
a(n) is the number of ones in the binary expansion of n^(n^n).
[ "1", "1", "30", "1", "3683", "36635", "1156050", "1", "614037343", "11609679812", "493508438640" ]
[ "nonn", "base", "more" ]
27
1
3
[ "A000120", "A002488", "A214561", "A379446", "A379447", "A379448" ]
null
Hugo Pfoertner, Dec 24 2024
2024-12-28T05:47:27
oeisdata/seq/A379/A379448.seq
2f9f310bc519e77a95c325d6b621cee2
A379449
Numbers k such that the prime gap between the consecutive primes p1 < k! = factorial(k) < p2 sets a new record.
[ "3", "4", "5", "8", "13", "19", "24", "29", "34", "45", "47", "51", "56", "61", "71", "107", "127", "140", "184", "192", "198", "274", "284", "375", "384", "559", "592", "630", "689", "774", "792", "834", "1133", "1213", "1241", "1315", "1947" ]
[ "nonn", "more" ]
14
1
1
[ "A054588", "A350100", "A378429", "A379449" ]
null
Jean-Marc Rebert, Dec 23 2024
2025-01-07T08:40:22
oeisdata/seq/A379/A379449.seq
65c21897e5862c00f7b3bb014aaa640b
A379450
a(n) is the smallest prime p such that omega(p^n - 1) is equal to n, where omega = A001221.
[ "3", "5", "7", "11", "31", "11", "79", "47", "211", "113", "2473", "47", "45841", "389", "1123", "1061" ]
[ "nonn", "more" ]
19
1
1
[ "A001221", "A219019", "A379450" ]
null
Juri-Stepan Gerasimov, Dec 23 2024
2025-01-05T23:42:02
oeisdata/seq/A379/A379450.seq
427c03671b2dbca69fa1fd73d5da7c96
A379451
Number of ordered ways of writing 0 as Sum_{k=-n..n} e(k)*k, where e(k) is 0 or 1.
[ "2", "10", "162", "6278", "430906", "46032666", "7029940154", "1453778429782", "390651831405906", "132345369222827306", "55150093300481888770", "27727437337790844360198", "16545310955942988999292586", "11561068480810074519638819626", "9349537740123803513263001013354", "8664632430514446774520557369434870" ]
[ "nonn" ]
11
0
1
[ "A000980", "A058377", "A063865", "A379451" ]
null
Ilya Gutkovskiy, Dec 23 2024
2024-12-23T22:05:59
oeisdata/seq/A379/A379451.seq
fa85218e5d2cd3ff92a2cba6b1e0bfb1
A379452
Number of compositions (ordered partitions) of 1 into n distinct reciprocals of positive integers.
[ "1", "0", "6", "144", "8640", "1670400", "1238655600", "6095673521280" ]
[ "nonn", "hard", "more" ]
4
1
3
[ "A002966", "A002967", "A006585", "A379452" ]
null
Ilya Gutkovskiy, Dec 23 2024
2024-12-23T22:06:11
oeisdata/seq/A379/A379452.seq
4dd5a247c640265d18730928f1164ccc
A379453
Numbers that decrease when they are replaced by the "Look and Say" description (cf. A045918) of their prime factors, counted with multiplicity.
[ "49", "64", "81", "125", "128", "243", "256", "289", "343", "361", "512", "529", "625", "729", "841", "961", "1024", "1250", "1331", "1369", "1458", "1681", "1715", "1849", "1875", "2048", "2187", "2197", "2209", "2401", "2500", "2809", "2916", "3087", "3125", "3375", "3481", "3721", "4096", "4374", "4489", "4802", "4913", "5000", "5041", "5329", "5488", "5625", "5832", "6075", "6125", "6241", "6250", "6561", "6859", "6889", "7203", "7776", "7921", "8000", "8192", "8575", "8748" ]
[ "nonn", "base" ]
12
1
1
[ "A005150", "A045918", "A367974", "A369092", "A369132", "A379453", "A379454", "A379455" ]
null
Scott R. Shannon, Dec 23 2024
2024-12-23T18:01:29
oeisdata/seq/A379/A379453.seq
c0c832bc30b8dbf058d1fdfcbd0eae2c
A379454
Numbers that decrease three times in succession when they are iteratively replaced by the "Look and Say" description (cf. A045918) of their prime factors, counted with multiplicity.
[ "727974361", "2204693643", "2643690625" ]
[ "nonn", "more", "bref", "base" ]
7
1
1
[ "A005150", "A045918", "A367974", "A369092", "A369132", "A379453", "A379454", "A379455" ]
null
Scott R. Shannon, Dec 23 2024
2024-12-23T09:51:29
oeisdata/seq/A379/A379454.seq
26f052e371d4f720a6c7d7f7d9f68e0d
A379455
Numbers that decrease two times in succession when they are iteratively replaced by the "Look and Say" description (cf. A045918) of their prime factors, counted with multiplicity.
[ "1849", "7921", "38809", "79507", "146529", "160801", "200978", "226981", "327697", "654481", "1113032", "1653125", "1731619", "1765376", "2109375", "2588881", "3418927", "3857868", "4182703", "5640625", "6492304", "6553600", "6892100", "7103125", "7845601", "8438707", "9509327", "11039981", "11880448", "12068352", "12106067", "12584111", "13227109", "14895500", "16843208", "17149469", "17372224", "18081075", "18852697", "19523584" ]
[ "nonn" ]
10
1
1
[ "A005150", "A045918", "A367974", "A369092", "A369132", "A379453", "A379454", "A379455" ]
null
Scott R. Shannon, Dec 23 2024
2024-12-23T09:52:01
oeisdata/seq/A379/A379455.seq
696421cd577d668f0c8746ea00cbb495
A379456
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) / (1 + x*exp(x)) ).
[ "1", "2", "13", "151", "2573", "58221", "1648345", "56138461", "2236816825", "102135829609", "5259937376141", "301678137203433", "19072415186892325", "1317869007328182349", "98818139178323981473", "7991908824553634264101", "693473520767940388417265", "64266613784795934251538513" ]
[ "nonn" ]
17
0
2
[ "A088690", "A108919", "A161633", "A379456", "A379699", "A379700", "A379846", "A379847" ]
null
Seiichi Manyama, Dec 30 2024
2025-02-05T09:22:39
oeisdata/seq/A379/A379456.seq
bf7257f86b02e0bb089559ca615d470e
A379457
If n = Product (p_j^k_j) then a(n) = Product (floor(p_j^(1/k_j))).
[ "1", "2", "3", "1", "5", "6", "7", "1", "1", "10", "11", "3", "13", "14", "15", "1", "17", "2", "19", "5", "21", "22", "23", "3", "2", "26", "1", "7", "29", "30", "31", "1", "33", "34", "35", "1", "37", "38", "39", "5", "41", "42", "43", "11", "5", "46", "47", "3", "2", "4", "51", "13", "53", "2", "55", "7", "57", "58", "59", "15", "61", "62", "7", "1", "65", "66", "67", "17", "69", "70", "71", "1", "73", "74", "6", "19", "77", "78", "79", "5" ]
[ "nonn", "mult" ]
4
1
2
[ "A005117", "A379457" ]
null
Ilya Gutkovskiy, Dec 23 2024
2024-12-23T22:06:19
oeisdata/seq/A379/A379457.seq
500abcc3ad55d5078fda80c734a17a06
A379458
Array read by downward antidiagonals: A(n,k) = A(n-1,k+1) + 2*(k+1)!*Sum_{j=0..k} A(n-1,j)/j! with A(0,k) = 1, n >= 0, k >= 0.
[ "1", "1", "3", "1", "9", "15", "1", "31", "79", "109", "1", "129", "459", "835", "1053", "1", "651", "3003", "6885", "10661", "12767", "1", "3913", "22183", "61735", "114373", "161229", "186763", "1", "27399", "183975", "603565", "1307997", "2134803", "2830787", "3204313", "1", "219201", "1698819", "6424059", "15981869", "29753069", "44649839", "56720039", "63128665" ]
[ "nonn", "tabl" ]
5
0
3
[ "A217061", "A379458" ]
null
Mikhail Kurkov, Dec 23 2024
2025-01-03T02:03:11
oeisdata/seq/A379/A379458.seq
9515f8fd17e7ebe8c36ac4bf36096aab
A379459
Array read by downward antidiagonals: A(n,k) = A(n-1,k+1) + 2*(k+1)!*Sum_{j=0..k} A(n-1,j)/j! with A(0,k) = 2*(k+1)!, n >= 0, k >= 0.
[ "2", "4", "8", "12", "36", "52", "48", "192", "368", "472", "240", "1200", "2880", "4560", "5504", "1440", "8640", "24960", "47280", "67408", "78416", "10080", "70560", "238560", "527520", "871584", "1163232", "1320064", "80640", "645120", "2499840", "6330240", "11926656", "18031104", "22997696", "25637824", "725760", "6531840", "28546560", "81527040", "172811520", "292642560", "415728960", "513000000", "564275648" ]
[ "nonn", "tabl" ]
4
0
1
[ "A006351", "A379459" ]
null
Mikhail Kurkov, Dec 23 2024
2025-01-03T02:03:22
oeisdata/seq/A379/A379459.seq
e7e8d4237baf7e2382d6934929abb3b2
A379460
Array read by downward antidiagonals: A(n,k) = A(n,k-1) + (k+1)*(A(n-1,k) + A(n-1,k+1)) with A(n,0) = A(n-1,0) + A(n-1,1), A(0,k) = 1, n >= 0, k >= 0.
[ "1", "1", "2", "1", "6", "8", "1", "12", "44", "52", "1", "20", "140", "420", "472", "1", "30", "340", "1860", "5032", "5504", "1", "42", "700", "6020", "28672", "72912", "78416", "1", "56", "1288", "15960", "116592", "508704", "1241648", "1320064", "1", "72", "2184", "36792", "380352", "2496480", "10257200", "24317760", "25637824", "1", "90", "3480", "76440", "1059744", "9696960", "59030960", "232182240", "538637824", "564275648" ]
[ "nonn", "tabl" ]
4
0
3
[ "A006351", "A379460" ]
null
Mikhail Kurkov, Dec 23 2024
2025-01-03T02:03:31
oeisdata/seq/A379/A379460.seq
2084431e3fd7477356e0b8d40031b4dd
A379461
Irregular triangle read by rows in which row n lists the divisors m of n such that there is a divisor d of n with d < m < 2*d, or 0 if such divisors do not exist.
[ "0", "0", "0", "0", "0", "3", "0", "0", "0", "0", "0", "3", "4", "6", "0", "0", "5", "0", "0", "3", "9", "0", "5", "0", "0", "0", "3", "4", "6", "8", "12", "0", "0", "0", "7", "0", "3", "5", "6", "10", "15", "0", "0", "0", "0", "7", "3", "4", "6", "9", "12", "18", "0", "0", "0", "5", "8", "10", "0", "3", "7", "21", "0", "0", "5", "9", "15", "0", "0", "3", "4", "6", "8", "12", "16", "24", "0", "0", "0", "0", "0", "3", "9", "27", "0" ]
[ "nonn", "tabf", "changed" ]
39
1
6
[ "A005279", "A027750", "A174903", "A174905", "A182469", "A237271", "A379288", "A379374", "A379379", "A379384", "A379461", "A383209" ]
null
Omar E. Pol, Dec 23 2024
2025-04-26T00:34:35
oeisdata/seq/A379/A379461.seq
3ad12342b934454723580a0c3ce073fd
A379462
a(n) is the total number of paths starting at (0, 0), ending at (n, 0), consisting of steps (1, 1), (1, 0), (1, -2), and staying on or above y = -3.
[ "1", "1", "1", "4", "13", "31", "75", "204", "561", "1499", "4001", "10814", "29364", "79704", "216672", "590764", "1614421", "4419049", "12116139", "33277722", "91546143", "252209535", "695803659", "1922166420", "5316714156", "14723570406", "40820144106", "113293243636", "314759548879", "875342190283", "2436582442381" ]
[ "nonn" ]
14
0
4
[ "A071879", "A116411", "A378849", "A378850", "A379462" ]
null
Emely Hanna Li Lobnig, Dec 23 2024
2025-01-28T03:48:25
oeisdata/seq/A379/A379462.seq
cca094559d870edc887c36058a9dd516
A379463
a(n) is the total number of paths starting at (0, 0), ending at (n, 0), consisting of steps (1, 1), (1, 0), (1, -3), and staying on or above y = -1.
[ "1", "1", "1", "1", "3", "11", "31", "71", "150", "334", "826", "2146", "5498", "13690", "33762", "84306", "214451", "551107", "1417291", "3637627", "9343555", "24096675", "62439587", "162331747", "422773098", "1102422546", "2879207046", "7534606366", "19756893196", "51894005428", "136496647696", "359478351816", "947912008073" ]
[ "nonn" ]
16
0
5
[ "A069271", "A127902", "A379463", "A379464" ]
null
Emely Hanna Li Lobnig, Dec 23 2024
2025-01-29T08:53:06
oeisdata/seq/A379/A379463.seq
390bf0cef9fa68e854bd80593b49ea22
A379464
a(n) is the total number of paths starting at (0, 0), ending at (n, 0), consisting of steps (1, 1), (1, 0), (1, -3), and staying on or above y = -2.
[ "1", "1", "1", "1", "4", "16", "46", "106", "226", "514", "1306", "3466", "9002", "22634", "56330", "142026", "364743", "945303", "2448511", "6323695", "16336885", "42363693", "110340297", "288229377", "753920796", "1973799396", "5174280216", "13588243696", "35748326836", "94188788164", "248464963876", "656148369796" ]
[ "nonn" ]
20
0
5
[ "A127902", "A379463", "A379464" ]
null
Emely Hanna Li Lobnig, Dec 23 2024
2025-01-29T08:58:29
oeisdata/seq/A379/A379464.seq
ae5359c822a654b74ffbf90861a110ae
A379465
Sum of coreful divisors d | k such that gcd(d, k/d) is not in {1, d, k/d} and rad(d) = rad(k/d), where k is in A376936 and rad = A007947.
[ "30", "42", "66", "126", "70", "78", "198", "264", "90", "234", "126", "120", "462", "312", "270", "270", "306", "150", "154", "696", "798", "936", "390", "210", "210", "290", "210", "714", "210", "286", "210", "462", "744", "240", "1710", "1224", "910", "330", "420", "2262", "390", "270", "714", "870", "1050", "294", "330", "630", "630", "2232", "378", "1620", "330" ]
[ "nonn" ]
41
1
1
[ "A364988", "A379465", "A379552" ]
null
Michael De Vlieger, Jan 13 2025
2025-01-19T09:29:32
oeisdata/seq/A379/A379465.seq
b9c685aefbc8967c21d5c483c692fcb8
A379466
Taxicab numbers that are abundant.
[ "4104", "13832", "32832", "39312", "64232", "65728", "110656", "110808", "165464", "171288", "262656", "314496", "320264", "373464", "513000", "513856", "525824", "805688", "885248", "886464", "955016", "994688", "1009736", "1016496", "1061424", "1075032", "1092728", "1323712", "1331064", "1370304", "1407672", "1609272", "1728216", "1729000", "1734264", "1774656", "2101248" ]
[ "nonn" ]
11
1
1
[ "A001235", "A005101", "A379466" ]
null
Massimo Kofler, Dec 23 2024
2025-01-29T09:26:43
oeisdata/seq/A379/A379466.seq
291d5e13cc4e8111a665cbf02f690723
A379467
Decimal expansion of (1 + sqrt(3))/3.
[ "9", "1", "0", "6", "8", "3", "6", "0", "2", "5", "2", "2", "9", "5", "9", "0", "9", "7", "8", "4", "2", "4", "8", "2", "1", "1", "3", "8", "3", "5", "2", "9", "0", "7", "8", "8", "9", "8", "0", "9", "3", "5", "0", "8", "4", "6", "0", "3", "4", "6", "0", "2", "0", "9", "3", "5", "1", "9", "3", "5", "6", "5", "9", "8", "1", "7", "3", "1", "1", "0", "0", "5", "6", "3", "6", "2", "6", "6", "6", "7", "9", "0", "2", "7", "0", "4", "8", "7", "2", "8", "9", "1", "9", "0", "8", "2", "8", "5", "8", "5" ]
[ "nonn", "cons", "easy" ]
5
0
1
[ "A002194", "A090388", "A379467" ]
null
Stefano Spezia, Dec 23 2024
2024-12-23T17:48:34
oeisdata/seq/A379/A379467.seq
246fb3fd466c43350471fd1fd3f934af
A379468
Decimal expansion of sqrt(3)/(4 - sqrt(2)).
[ "6", "6", "9", "8", "3", "5", "2", "1", "2", "3", "6", "1", "3", "3", "4", "8", "0", "5", "1", "6", "4", "7", "9", "0", "6", "7", "4", "3", "3", "7", "8", "1", "2", "9", "1", "8", "5", "5", "2", "6", "5", "4", "8", "9", "2", "5", "6", "4", "1", "5", "6", "6", "1", "7", "1", "8", "9", "7", "0", "8", "6", "0", "6", "0", "7", "5", "6", "2", "0", "8", "8", "8", "9", "3", "5", "1", "7", "9", "6", "5", "5", "3", "4", "7", "4", "6", "0", "2", "9", "8", "5", "8", "0", "9", "7", "3", "8", "9", "5", "5" ]
[ "nonn", "cons", "easy" ]
5
0
1
[ "A002193", "A002194", "A379468" ]
null
Stefano Spezia, Dec 23 2024
2024-12-23T17:48:42
oeisdata/seq/A379/A379468.seq
ac0c79c743bf81967aa6d23ee92d8193
A379469
Decimal expansion of (1 + sqrt(6))/(3*sqrt(2)).
[ "8", "1", "3", "0", "5", "2", "5", "2", "9", "5", "8", "5", "1", "4", "1", "6", "0", "5", "9", "7", "6", "0", "9", "6", "9", "0", "1", "2", "0", "3", "5", "7", "3", "8", "0", "2", "0", "7", "5", "8", "8", "0", "3", "9", "7", "1", "6", "6", "2", "8", "4", "8", "8", "8", "2", "1", "4", "7", "1", "5", "6", "1", "6", "1", "4", "9", "0", "9", "9", "7", "5", "2", "0", "4", "6", "6", "1", "7", "8", "5", "2", "1", "6", "8", "7", "7", "9", "9", "8", "4", "6", "4", "0", "3", "5", "6", "4", "5", "4", "0" ]
[ "nonn", "cons", "easy" ]
14
0
1
[ "A002193", "A010464", "A010474", "A086180", "A379469" ]
null
Stefano Spezia, Dec 23 2024
2024-12-24T05:17:28
oeisdata/seq/A379/A379469.seq
64b4be1e8b010ee934078411d0fefedb
A379470
For n >= 1, a(n) = Sum_{i = 0..(n - 1)} n / GCD(n, i!).
[ "1", "4", "9", "12", "25", "18", "49", "28", "39", "40", "121", "40", "169", "70", "65", "62", "289", "66", "361", "80", "105", "154", "529", "84", "165", "208", "135", "126", "841", "110", "961", "132", "209", "340", "217", "132", "1369", "418", "273", "160", "1681", "168", "1849", "242", "207", "598", "2209", "174", "427", "240", "425", "312", "2809", "216", "385", "238" ]
[ "nonn" ]
9
1
2
[ "A000040", "A000142", "A379470" ]
null
Ctibor O. Zizka, Dec 23 2024
2024-12-23T22:05:01
oeisdata/seq/A379/A379470.seq
b686b5eefe4ccb70548bedc04199fdcc
A379471
Composition of bijective bit-reverse and Blue code, in this order: a(n) = A193231(A057889(n)).
[ "0", "1", "3", "2", "5", "4", "6", "7", "15", "14", "12", "11", "10", "13", "9", "8", "17", "16", "18", "31", "20", "21", "29", "26", "30", "19", "23", "28", "27", "22", "24", "25", "51", "50", "48", "35", "54", "61", "33", "44", "60", "55", "63", "38", "39", "56", "46", "41", "34", "49", "53", "32", "57", "62", "36", "47", "45", "52", "58", "37", "40", "59", "43", "42", "85", "84", "86", "103", "80", "69", "101", "118", "90", "91", "71", "104", "99", "74", "116", "121" ]
[ "nonn", "base", "easy" ]
9
0
3
[ "A057889", "A193231", "A379471", "A379472" ]
null
Antti Karttunen, Dec 25 2024
2024-12-25T10:54:43
oeisdata/seq/A379/A379471.seq
d10dfbb1335c405981b8e1b7f8e2091b
A379472
Composition of Blue code and bijective bit-reverse, in this order: a(n) = A057889(A193231(n)).
[ "0", "1", "3", "2", "5", "4", "6", "7", "15", "14", "12", "11", "10", "13", "9", "8", "17", "16", "18", "25", "20", "21", "29", "26", "30", "31", "23", "28", "27", "22", "24", "19", "51", "38", "48", "35", "54", "59", "43", "44", "60", "47", "63", "62", "39", "56", "46", "55", "34", "49", "33", "32", "57", "50", "36", "41", "45", "52", "58", "61", "40", "37", "53", "42", "85", "84", "106", "117", "80", "69", "101", "74", "90", "109", "77", "104", "125", "122", "116", "93" ]
[ "nonn", "easy", "base" ]
9
0
3
[ "A057889", "A193231", "A379471", "A379472" ]
null
Antti Karttunen, Dec 25 2024
2024-12-25T10:54:52
oeisdata/seq/A379/A379472.seq
a30d699b1727423bb120d46181c80db2
A379473
a(n) is the highest power of 3 dividing the sum of divisors of n.
[ "1", "3", "1", "1", "3", "3", "1", "3", "1", "9", "3", "1", "1", "3", "3", "1", "9", "3", "1", "3", "1", "9", "3", "3", "1", "3", "1", "1", "3", "9", "1", "9", "3", "27", "3", "1", "1", "3", "1", "9", "3", "3", "1", "3", "3", "9", "3", "1", "3", "3", "9", "1", "27", "3", "9", "3", "1", "9", "3", "3", "1", "3", "1", "1", "3", "9", "1", "9", "3", "9", "9", "3", "1", "3", "1", "1", "3", "3", "1", "3", "1", "9", "3", "1", "27", "3", "3", "9", "9", "9", "1", "3", "1", "9", "3", "9", "1", "9", "3", "1", "3", "27", "1", "3", "3" ]
[ "nonn", "mult" ]
9
1
2
[ "A000203", "A000244", "A038500", "A082903", "A087943", "A329963", "A354100", "A379473", "A379481", "A379484" ]
null
Antti Karttunen, Dec 27 2024
2024-12-27T18:08:53
oeisdata/seq/A379/A379473.seq
9983bfd357c8a01275d588d818c0898f
A379474
Number of prime factors of the form p^e || n : [p == 1 (mod 8), e == 1 (mod 4)] or [p == 5 (mod 8), e == -1 (mod 4)].
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1" ]
[ "nonn" ]
16
1
697
[ "A379474", "A379949" ]
null
Antti Karttunen, Jan 07 2025
2025-01-07T15:55:29
oeisdata/seq/A379/A379474.seq
d710f1c09e29e12fc56340555a00d100
A379475
a(n) = 1 if A372565(n) > 1, otherwise 0, where A372565(n) is the greatest common divisor of n, sigma(n) and A003961(n).
[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1" ]
[ "nonn" ]
12
1
null
[ "A000203", "A003961", "A296210", "A325964", "A349167", "A372565", "A372566", "A379475", "A379476" ]
null
Antti Karttunen, Dec 23 2024
2024-12-23T15:11:06
oeisdata/seq/A379/A379475.seq
28d50f4980b60a02b7482c256058b137
A379476
a(n) = 1 if A326057(n) > 1, otherwise 0, where A326057(n) = gcd(A003961(n)-2n, A003961(n)-sigma(n)).
[ "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "1", "1", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1" ]
[ "nonn" ]
6
1
null
[ "A000203", "A003961", "A252748", "A286385", "A326057", "A379475", "A379476", "A379477" ]
null
Antti Karttunen, Dec 23 2024
2024-12-23T15:11:10
oeisdata/seq/A379/A379476.seq
daa2dd25738cf95388db38cd464c37c2
A379477
Numbers k such that A003961(k)-2k and A003961(k)-sigma(k) have a common divisor > 1, where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.
[ "6", "7", "13", "18", "19", "24", "28", "30", "31", "37", "42", "43", "46", "54", "55", "60", "61", "66", "67", "68", "69", "72", "78", "79", "90", "91", "96", "97", "102", "103", "106", "109", "114", "120", "126", "127", "131", "132", "135", "138", "139", "140", "146", "150", "151", "162", "163", "166", "168", "174", "175", "180", "181", "186", "193", "198", "199", "200", "204", "210", "216", "222", "223", "229", "234", "240", "241", "246", "251" ]
[ "nonn" ]
17
1
1
[ "A000203", "A000396", "A003961", "A252748", "A286385", "A326057", "A372566", "A378980", "A379476", "A379477", "A379479" ]
null
Antti Karttunen, Dec 23 2024
2024-12-23T17:48:47
oeisdata/seq/A379/A379477.seq
9922900843b619efd08671176c6ad0d9
A379478
a(n) = 1 if the greatest common divisor of n, sigma(n) and A003961(n) is 1 and gcd(A003961(n)-2n, A003961(n)-sigma(n)) > 1, otherwise 0.
[ "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ]
[ "nonn" ]
8
1
null
[ "A000203", "A003961", "A326057", "A372565", "A379475", "A379476", "A379478", "A379479" ]
null
Antti Karttunen, Dec 23 2024
2024-12-23T17:48:51
oeisdata/seq/A379/A379478.seq
e07a54582281a12342e43085b45fc74c
A379479
Numbers k such that the greatest common divisor of k, sigma(k) and A003961(k) is 1 and gcd(A003961(k)-2k, A003961(k)-sigma(k)) > 1.
[ "7", "13", "19", "28", "31", "37", "43", "46", "55", "61", "67", "68", "69", "79", "91", "97", "103", "106", "109", "127", "131", "139", "146", "151", "163", "166", "175", "181", "193", "199", "200", "223", "229", "241", "251", "261", "271", "277", "283", "301", "307", "313", "323", "325", "331", "337", "344", "346", "349", "371", "379", "391", "397", "409", "421", "428", "439", "444", "449", "457", "463", "466", "475", "481", "487", "491", "494", "496" ]
[ "nonn" ]
11
1
1
[ "A000203", "A000396", "A003961", "A104210", "A319630", "A326057", "A372565", "A372566", "A379477", "A379478", "A379479" ]
null
Antti Karttunen, Dec 23 2024
2024-12-23T17:48:55
oeisdata/seq/A379/A379479.seq
a6aaa0e6377b840474e6ded62cab7e70
A379480
a(n) = 1 if n is twice a square, otherwise 0.
[ "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ]
[ "nonn" ]
10
0
null
[ "A001105", "A010052", "A053866", "A093709", "A379480" ]
null
Antti Karttunen, Jan 19 2025
2025-01-23T10:23:03
oeisdata/seq/A379/A379480.seq
3788da136f52ec81f7a6b6e611162efb
A379481
Square of prime-shifted n, or equally, n squared, then prime-shifted one step towards larger primes.
[ "1", "9", "25", "81", "49", "225", "121", "729", "625", "441", "169", "2025", "289", "1089", "1225", "6561", "361", "5625", "529", "3969", "3025", "1521", "841", "18225", "2401", "2601", "15625", "9801", "961", "11025", "1369", "59049", "4225", "3249", "5929", "50625", "1681", "4761", "7225", "35721", "1849", "27225", "2209", "13689", "30625", "7569", "2809", "164025", "14641", "21609", "9025", "23409", "3481", "140625" ]
[ "nonn", "easy", "mult" ]
20
1
2
[ "A000290", "A003961", "A016754", "A048673", "A111003", "A337336", "A378231", "A379473", "A379481", "A379482", "A379484" ]
null
Antti Karttunen, Dec 27 2024
2024-12-28T09:11:54
oeisdata/seq/A379/A379481.seq
ac1ca17ce479c7a9bf3b9d5d6cbd1b03
A379482
a(n) = sigma(A003961(n^2)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.
[ "1", "13", "31", "121", "57", "403", "133", "1093", "781", "741", "183", "3751", "307", "1729", "1767", "9841", "381", "10153", "553", "6897", "4123", "2379", "871", "33883", "2801", "3991", "19531", "16093", "993", "22971", "1407", "88573", "5673", "4953", "7581", "94501", "1723", "7189", "9517", "62301", "1893", "53599", "2257", "22143", "44517", "11323", "2863", "305071", "16105", "36413", "11811", "37147", "3541" ]
[ "nonn", "mult" ]
17
1
2
[ "A000290", "A003973", "A038500", "A048673", "A151800", "A337336", "A337337", "A378231", "A379223", "A379481", "A379482", "A379483", "A379484" ]
null
Antti Karttunen, Dec 27 2024
2024-12-27T18:18:24
oeisdata/seq/A379/A379482.seq
488c311ca49e81bd6d731281f95957d7
A379483
a(n) is the number of trailing 1-bits in the binary representation of sigma(A003961(n^2)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.
[ "1", "1", "5", "1", "1", "2", "1", "1", "1", "1", "3", "3", "2", "1", "3", "1", "1", "1", "1", "1", "2", "2", "3", "2", "1", "3", "2", "1", "1", "2", "7", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "5", "1", "7", "1", "2", "4", "4", "1", "1", "2", "2", "1", "4", "6", "1", "3", "1", "3", "4", "1", "2", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "7", "4", "1", "2", "1", "1", "1", "1", "1", "2", "2", "1", "1", "6", "2", "2", "1", "7", "4", "1", "2", "1", "2", "6", "1", "2", "1", "1", "3", "1", "6", "2" ]
[ "nonn" ]
10
1
3
[ "A003961", "A003973", "A007814", "A048673", "A336700", "A379222", "A379482", "A379483" ]
null
Antti Karttunen, Dec 27 2024
2024-12-27T18:25:32
oeisdata/seq/A379/A379483.seq
ca95933529aacaba1f331e06a6a07cca
A379484
a(n) is the highest power of 3 dividing sigma(A003961(n^2)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and sigma is the sum of divisors function.
[ "1", "1", "1", "1", "3", "1", "1", "1", "1", "3", "3", "1", "1", "1", "3", "1", "3", "1", "1", "3", "1", "3", "1", "1", "1", "1", "1", "1", "3", "3", "3", "1", "3", "3", "3", "1", "1", "1", "1", "3", "3", "1", "1", "3", "3", "1", "1", "1", "1", "1", "3", "1", "1", "1", "9", "1", "1", "3", "3", "3", "3", "3", "1", "1", "3", "3", "1", "3", "1", "3", "3", "1", "3", "1", "1", "1", "3", "1", "1", "3", "1", "3", "1", "1", "9", "1", "3", "3", "3", "3", "1", "1", "3", "1", "3", "1", "1", "1", "3", "1", "3", "3", "1", "1", "3" ]
[ "nonn", "mult" ]
8
1
5
[ "A038500", "A151800", "A379473", "A379481", "A379482", "A379484" ]
null
Antti Karttunen, Dec 27 2024
2024-12-27T18:27:07
oeisdata/seq/A379/A379484.seq
2e626751a7799a232a34ad1b15fa06d8
A379485
a(n) = 1 if gcd(n,A003961(n))*gcd(sigma(n),A276086(n)) is equal to gcd(n,A276086(n))*gcd(sigma(n),A003961(n)), otherwise 0, where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.
[ "1", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1" ]
[ "nonn" ]
8
1
null
[ "A000203", "A003961", "A276086", "A379485", "A379486" ]
null
Antti Karttunen, Jan 01 2025
2025-01-01T20:38:22
oeisdata/seq/A379/A379485.seq
b8ae2cbf1aee0f8d5159ee3c2ad124a1
A379486
Numbers k for which gcd(k,A003961(k))*gcd(sigma(k),A276086(k)) is equal to gcd(k,A276086(k))*gcd(sigma(k),A003961(k)), where A003961(n) is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.
[ "1", "2", "4", "6", "14", "16", "18", "24", "26", "28", "40", "54", "62", "64", "66", "74", "86", "102", "114", "122", "134", "138", "146", "152", "162", "169", "174", "176", "182", "184", "186", "206", "222", "234", "254", "270", "280", "282", "289", "290", "302", "304", "306", "308", "314", "318", "326", "338", "342", "354", "360", "361", "366", "368", "380", "384", "386", "402", "414", "422", "426", "434", "438", "441", "446", "448", "456", "474", "496" ]
[ "nonn" ]
13
1
2
[ "A000203", "A003961", "A007691", "A276086", "A322361", "A324198", "A324644", "A342671", "A379485", "A379486", "A379487", "A379488", "A379489", "A379491" ]
null
Antti Karttunen, Jan 01 2025
2025-01-02T13:03:26
oeisdata/seq/A379/A379486.seq
912b4f8c7ad921e69853408ce1f5cb15
A379487
a(n) = gcd(n,A003961(n)) * gcd(sigma(n),A276086(n)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.
[ "1", "3", "2", "1", "6", "3", "2", "15", "1", "9", "6", "3", "2", "3", "30", "1", "18", "3", "10", "3", "2", "9", "6", "15", "1", "3", "10", "1", "30", "15", "2", "21", "6", "9", "42", "63", "2", "15", "14", "45", "42", "3", "2", "21", "30", "9", "6", "3", "1", "3", "6", "7", "18", "15", "2", "15", "10", "45", "30", "105", "2", "3", "2", "1", "42", "3", "2", "21", "6", "63", "18", "45", "2", "3", "10", "35", "66", "21", "10", "3", "1", "63", "42", "21", "2", "3", "30", "45", "90", "15", "14", "21" ]
[ "nonn" ]
8
1
2
[ "A000203", "A003961", "A276086", "A322361", "A324644", "A379486", "A379487", "A379488", "A379489" ]
null
Antti Karttunen, Jan 02 2025
2025-01-02T13:03:30
oeisdata/seq/A379/A379487.seq
3c8cfe07d508b8f8ae7ab3c65ab15c81
A379488
a(n) = gcd(n,A276086(n)) * gcd(sigma(n),A003961(n)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.
[ "1", "3", "3", "1", "1", "3", "1", "3", "3", "15", "1", "1", "1", "3", "15", "1", "1", "3", "1", "105", "3", "3", "1", "15", "25", "3", "15", "1", "1", "3", "1", "9", "3", "3", "7", "1", "1", "3", "3", "45", "1", "21", "1", "3", "15", "3", "1", "1", "7", "75", "3", "1", "1", "15", "5", "21", "15", "3", "1", "21", "1", "3", "21", "1", "7", "3", "1", "9", "3", "105", "1", "15", "1", "3", "75", "1", "7", "3", "1", "15", "3", "3", "1", "7", "5", "3", "15", "9", "1", "3", "7", "3", "3", "3", "1", "9", "1", "147" ]
[ "nonn" ]
9
1
2
[ "A000203", "A003961", "A276086", "A324198", "A342671", "A379486", "A379487", "A379488", "A379489" ]
null
Antti Karttunen, Jan 02 2025
2025-01-02T13:03:34
oeisdata/seq/A379/A379488.seq
e6b00b9380edbf62af272793b6126a4d
A379489
a(n) = gcd(n,A003961(n))*gcd(sigma(n),A276086(n)) - gcd(n,A276086(n))*gcd(sigma(n),A003961(n)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.
[ "0", "0", "-1", "0", "5", "0", "1", "12", "-2", "-6", "5", "2", "1", "0", "15", "0", "17", "0", "9", "-102", "-1", "6", "5", "0", "-24", "0", "-5", "0", "29", "12", "1", "12", "3", "6", "35", "62", "1", "12", "11", "0", "41", "-18", "1", "18", "15", "6", "5", "2", "-6", "-72", "3", "6", "17", "0", "-3", "-6", "-5", "42", "29", "84", "1", "0", "-19", "0", "35", "0", "1", "12", "3", "-42", "17", "30", "1", "0", "-65", "34", "59", "18", "9", "-12", "-2", "60", "41", "14", "-3", "0", "15" ]
[ "sign" ]
7
1
5
[ "A000203", "A003961", "A276086", "A379486", "A379487", "A379488", "A379489" ]
null
Antti Karttunen, Jan 02 2025
2025-01-02T13:03:39
oeisdata/seq/A379/A379489.seq
c0a5233d3f3c95bf4c63f9d9586678f2
A379490
Odd squares s such that 2*s is equal to bitwise-AND of 2*s and sigma(s).
[ "399736269009", "1013616036225", "1393148751631700625" ]
[ "nonn", "bref", "more" ]
12
1
1
[ "A000203", "A004198", "A005231", "A016754", "A318468", "A324647", "A325311", "A336700", "A336701", "A337339", "A337342", "A348742", "A379474", "A379490", "A379503", "A379505", "A379949" ]
null
Antti Karttunen, Jan 13 2025
2025-01-15T12:15:19
oeisdata/seq/A379/A379490.seq
09d27c0fcea26d799057816fc818beb4
A379491
Multiperfect numbers k for which gcd(k,A003961(k))*gcd(sigma(k),A276086(k)) is equal to gcd(k,A276086(k))*gcd(sigma(k),A003961(k)), where A003961(n) is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.
[ "1", "6", "28", "496", "8128", "30240", "32760", "2178540", "23569920", "33550336", "45532800", "142990848", "459818240", "1379454720", "8589869056", "43861478400", "51001180160", "66433720320", "137438691328", "153003540480", "403031236608", "704575228896", "181742883469056", "6088728021160320", "14942123276641920", "20158185857531904", "275502900594021408", "622286506811515392" ]
[ "nonn" ]
8
1
2
[ "A000203", "A003961", "A007691", "A276086", "A322361", "A323653", "A324198", "A324644", "A336702", "A342671", "A379485", "A379486", "A379487", "A379488", "A379491", "A379492" ]
null
Antti Karttunen, Jan 02 2025
2025-01-03T09:34:45
oeisdata/seq/A379/A379491.seq
63fcea560308e7debbd2239ef3549552
A379492
Multiperfect numbers k for which gcd(k,A003961(k))*gcd(sigma(k),A276086(k)) is not equal to gcd(k,A276086(k))*gcd(sigma(k),A003961(k)), where A003961(n) is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.
[ "120", "672", "523776", "1476304896", "14182439040", "31998395520", "518666803200", "13661860101120", "30823866178560", "740344994887680", "796928461056000", "212517062615531520", "69357059049509038080", "87934476737668055040", "154345556085770649600", "170206605192656148480", "1161492388333469337600", "1802582780370364661760", "9186050031556349952000" ]
[ "nonn" ]
8
1
1
[ "A000027", "A000203", "A003961", "A007691", "A046061", "A276086", "A322361", "A323653", "A324198", "A324644", "A342671", "A379485", "A379486", "A379487", "A379488", "A379491", "A379492" ]
null
Antti Karttunen, Jan 02 2025
2025-01-03T09:34:51
oeisdata/seq/A379/A379492.seq
d573c65ccd575fb41db01c887394229d
A379493
a(n) = A276086(A001065(n)), where A276086 is the primorial base exp-function, and A001065 is the sum of proper divisors of n.
[ "1", "2", "2", "6", "2", "5", "2", "10", "9", "15", "2", "225", "2", "45", "30", "150", "2", "750", "2", "1125", "90", "75", "2", "35", "5", "225", "50", "5625", "2", "175", "2", "14", "150", "375", "50", "8750", "2", "1125", "450", "2625", "2", "4375", "2", "315", "42", "1875", "2", "11025", "15", "350", "750", "1575", "2", "245", "450", "441", "2250", "21", "2", "42875", "2", "63", "630", "294", "250", "6125", "2", "39375", "3750", "3675", "2", "14406" ]
[ "nonn" ]
6
1
2
[ "A001065", "A276086", "A379493", "A379494" ]
null
Antti Karttunen, Jan 05 2025
2025-01-05T13:36:48
oeisdata/seq/A379/A379493.seq
65398d17001ed8fd198e07e7b230c8d3
A379494
a(n) = 2*A276086(n) - A276086(A001065(n)), where A276086 is the primorial base exp-function, and A001065 is the sum of proper divisors of n.
[ "3", "4", "10", "12", "34", "5", "18", "20", "51", "75", "178", "-175", "98", "105", "270", "300", "898", "-500", "498", "-375", "1410", "2175", "4498", "1215", "2495", "3525", "7450", "5625", "22498", "-161", "26", "28", "-66", "-249", "202", "-8680", "138", "-915", "-30", "-1995", "1258", "-4025", "698", "735", "2058", "1275", "6298", "-9275", "3485", "4900", "9750", "14175", "31498", "8505", "17050", "25809", "50250", "78729" ]
[ "sign" ]
6
1
1
[ "A001065", "A276086", "A379493", "A379494" ]
null
Antti Karttunen, Jan 05 2025
2025-01-05T13:36:54
oeisdata/seq/A379/A379494.seq
e5c87f9b82ff23e764fb848375e587e2
A379495
a(n) = A019565(A001065(n)), where A019565 is the base-2 exp-function, and A001065 is the sum of proper divisors of n.
[ "1", "2", "2", "6", "2", "15", "2", "30", "5", "7", "2", "11", "2", "21", "14", "210", "2", "110", "2", "165", "42", "105", "2", "65", "15", "11", "70", "385", "2", "273", "2", "2310", "210", "55", "70", "4290", "2", "165", "22", "429", "2", "2145", "2", "91", "26", "231", "2", "595", "7", "546", "110", "1365", "2", "51", "22", "17", "330", "13", "2", "7735", "2", "39", "182", "30030", "66", "1785", "2", "3003", "462", "357", "2", "102102", "2", "91", "286", "17", "66" ]
[ "nonn" ]
8
1
2
[ "A001065", "A019565", "A379493", "A379495", "A379496", "A379501" ]
null
Antti Karttunen, Jan 05 2025
2025-01-05T22:39:03
oeisdata/seq/A379/A379495.seq
f1d7ac89d7a3884a0f5379cbc9d6c35a
A379496
a(n) = A019565(1+n) - A019565(A001065(n)), where A019565 is the base-2 exp-function, and A001065 is the sum of proper divisors of n.
[ "2", "4", "3", "4", "13", "15", "5", "-16", "16", "35", "33", "59", "103", "189", "-3", "-188", "31", "-44", "53", "-55", "123", "225", "75", "89", "216", "451", "315", "385", "1153", "2037", "11", "-2284", "-171", "23", "-5", "-4160", "193", "225", "69", "-247", "271", "-1599", "453", "819", "1339", "2499", "141", "-309", "422", "312", "605", "65", "2143", "4239", "979", "1985", "2673", "5993", "5003", "2275", "15013", "29991", "-165" ]
[ "sign" ]
17
1
1
[ "A001065", "A016754", "A019565", "A379495", "A379496", "A379498", "A379501" ]
null
Antti Karttunen, Jan 05 2025
2025-01-05T22:35:32
oeisdata/seq/A379/A379496.seq
814a08d76695cb842a94201cbb731d8a
A379497
Dirichlet inverse of A046897, where A046897 is the sum of divisors of n that are not divisible by 4.
[ "1", "-3", "-4", "6", "-6", "12", "-8", "-12", "3", "18", "-12", "-24", "-14", "24", "24", "24", "-18", "-9", "-20", "-36", "32", "36", "-24", "48", "5", "42", "0", "-48", "-30", "-72", "-32", "-48", "48", "54", "48", "18", "-38", "60", "56", "72", "-42", "-96", "-44", "-72", "-18", "72", "-48", "-96", "7", "-15", "72", "-84", "-54", "0", "72", "96", "80", "90", "-60", "144", "-62", "96", "-24", "96", "84", "-144", "-68", "-108", "96", "-144", "-72", "-36" ]
[ "sign", "mult", "easy" ]
10
1
2
[ "A046897", "A379497" ]
null
Antti Karttunen, Jan 02 2025
2025-01-03T09:37:07
oeisdata/seq/A379/A379497.seq
1dffa82d763ca2feebdaa3eb0671b996
A379498
a(n) = A276086(1+n) - A276086(A001065(n)), where A276086 is the primorial base exp-function, and A001065 is the sum of proper divisors of n.
[ "2", "4", "7", "12", "3", "5", "13", "20", "36", "75", "23", "-175", "73", "105", "195", "300", "123", "-500", "373", "-375", "1035", "2175", "623", "1215", "1870", "3525", "5575", "5625", "5", "-161", "19", "28", "-87", "-249", "-15", "-8680", "103", "-915", "-135", "-1995", "173", "-4025", "523", "735", "1533", "1275", "873", "-9275", "2610", "4900", "7125", "14175", "4373", "8505", "12675", "25809", "37125", "78729", "47" ]
[ "sign" ]
7
1
1
[ "A001065", "A276086", "A379493", "A379494", "A379496", "A379498" ]
null
Antti Karttunen, Jan 05 2025
2025-01-05T22:35:28
oeisdata/seq/A379/A379498.seq
2d9fb571b01dc14ada95214ada4f0064
A379499
Square array A(n, k) = A064987(A246278(n, k)), read by falling antidiagonals; A064987(n) = n*sigma(n), applied to the prime shift array.
[ "6", "28", "12", "72", "117", "30", "120", "360", "775", "56", "180", "1080", "1680", "2793", "132", "336", "672", "19500", "7392", "16093", "182", "336", "3510", "3960", "137200", "24024", "30927", "306", "496", "1584", "43400", "10192", "1948584", "55692", "88723", "380", "702", "9801", "5460", "368676", "40392", "5228860", "116280", "137541", "552", "840", "9300", "488125", "17136", "2928926", "69160", "25645860", "209760", "292537", "870" ]
[ "nonn", "tabl" ]
8
1
1
[ "A000203", "A003961", "A064987", "A246278", "A355927", "A379499", "A379500" ]
null
Antti Karttunen, Jan 02 2025
2025-01-03T09:32:22
oeisdata/seq/A379/A379499.seq
1c3a6ce3027ca5a34cc41f4606b168a2
A379500
Square array A(n, k) = A249670(A246278(n, k)), read by falling antidiagonals; A249670(n) = A017665(n)*A017666(n), applied to the prime shift array.
[ "6", "28", "12", "2", "117", "30", "120", "40", "775", "56", "45", "1080", "1680", "2793", "132", "21", "672", "19500", "7392", "16093", "182", "84", "390", "3960", "137200", "24024", "30927", "306", "496", "176", "43400", "208", "1948584", "55692", "88723", "380", "78", "9801", "5460", "368676", "40392", "5228860", "116280", "137541", "552", "210", "9300", "488125", "17136", "2928926", "69160", "25645860", "209760", "292537", "870" ]
[ "nonn", "tabl" ]
11
1
1
[ "A036690", "A246278", "A249670", "A341605", "A341606", "A355925", "A361468", "A379499", "A379500" ]
null
Antti Karttunen, Jan 02 2025
2025-01-03T09:32:28
oeisdata/seq/A379/A379500.seq
b765f7263ac47101195c8478c45d64a7
A379501
a(n) = (3/2)*A019565((2n-1)^2) - A019565(A001065((2n-1)^2)), where A019565 is the base-2 exp-function, and A001065 is the sum of proper divisors of n.
[ "2", "16", "216", "422", "470", "51016", "5082", "4446", "864", "106688", "1301846", "880", "204182", "1985872", "236964", "646310", "1030", "176778", "2799756", "96178962", "563400", "62092576", "1566805968", "27274", "559406", "-16252236", "1040774592", "263042394", "7794826", "115781204", "13256922", "-16386856", "-1230440", "376172", "-67188814", "222905278", "13547232", "28352541646" ]
[ "sign" ]
16
1
1
[ "A001065", "A016754", "A019565", "A337339", "A378231", "A379495", "A379496", "A379501" ]
null
Antti Karttunen, Jan 05 2025
2025-01-05T22:38:56
oeisdata/seq/A379/A379501.seq
dde4cb24cd083077e5ef2255a798734e