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oeis

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1999-12-11 03:00:00
2025-04-25 01:21:50
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A359901
Triangle read by rows where T(n,k) is the number of integer partitions of n with median k = 1..n.
[ "1", "1", "1", "1", "0", "1", "2", "2", "0", "1", "3", "1", "0", "0", "1", "4", "2", "3", "0", "0", "1", "6", "3", "1", "0", "0", "0", "1", "8", "6", "2", "4", "0", "0", "0", "1", "11", "7", "3", "1", "0", "0", "0", "0", "1", "15", "10", "4", "2", "5", "0", "0", "0", "0", "1", "20", "13", "7", "3", "1", "0", "0", "0", "0", "0", "1", "26", "19", "11", "4", "2", "6", "0", "0", "0", "0", "0", "1" ]
[ "nonn", "tabl" ]
9
0
5
[ "A000009", "A000041", "A008284", "A008289", "A026424", "A027193", "A027336", "A058398", "A067538", "A067659", "A102627", "A237984", "A240219", "A316413", "A325347", "A326567", "A326568", "A327472", "A327482", "A349156", "A359889", "A359893", "A359894", "A359901", "A359902", "A359907", "A360005", "A360006", "A360007" ]
null
Gus Wiseman, Jan 21 2023
2023-02-23T21:24:49
oeisdata/seq/A359/A359901.seq
88daae99285ec143b7a2a154f70e455e
A359902
Triangle read by rows where T(n,k) is the number of odd-length integer partitions of n with median k.
[ "1", "0", "1", "1", "0", "1", "1", "0", "0", "1", "2", "1", "0", "0", "1", "2", "2", "0", "0", "0", "1", "4", "2", "1", "0", "0", "0", "1", "4", "3", "2", "0", "0", "0", "0", "1", "7", "4", "3", "1", "0", "0", "0", "0", "1", "8", "6", "3", "2", "0", "0", "0", "0", "0", "1", "12", "8", "4", "3", "1", "0", "0", "0", "0", "0", "1", "14", "11", "5", "4", "2", "0", "0", "0", "0", "0", "0", "1" ]
[ "nonn", "tabl" ]
6
0
5
[ "A000009", "A000041", "A002865", "A008284", "A008289", "A026424", "A027193", "A058398", "A067538", "A067659", "A102627", "A240219", "A307683", "A316413", "A325347", "A326567", "A326568", "A327472", "A327482", "A359889", "A359893", "A359894", "A359895", "A359901", "A359902", "A359906", "A359907", "A359910", "A360005", "A360006", "A360007" ]
null
Gus Wiseman, Jan 21 2023
2023-01-22T09:16:44
oeisdata/seq/A359/A359902.seq
19e0cd3802e54fc2a0a65d52777efb45
A359903
Numbers whose prime indices and prime signature have the same mean.
[ "1", "2", "9", "88", "100", "125", "624", "756", "792", "810", "880", "900", "1312", "2401", "4617", "4624", "6240", "7392", "7560", "7920", "8400", "9261", "9604", "9801", "10648", "12416", "23424", "33984", "37760", "45792", "47488", "60912", "66176", "71552", "73920", "75200", "78720", "83592", "89216", "89984", "91264", "91648", "99456" ]
[ "nonn" ]
7
0
5
[ "A001222", "A008284", "A056239", "A058398", "A067340", "A088529", "A088530", "A112798", "A124010", "A240219", "A316313", "A316413", "A326567", "A326568", "A326622", "A327473", "A327476", "A327482", "A348551", "A359903", "A359904", "A359905", "A359908", "A360005", "A360008", "A360068", "A360069" ]
null
Gus Wiseman, Jan 24 2023
2023-01-26T10:04:23
oeisdata/seq/A359/A359903.seq
573092721f984e85779859573266db2e
A359904
Numbers whose prime factors and prime signature have the same mean.
[ "1", "4", "27", "400", "3125", "9072", "10800", "14580", "24057", "35721", "50625", "73984", "117760", "134400", "158976", "181440", "191488", "389376", "452709", "544000", "583680", "664848", "731136", "774400", "823543", "878592", "965888" ]
[ "nonn" ]
7
0
5
[ "A001222", "A008284", "A027746", "A056239", "A058398", "A067340", "A078175", "A088529", "A088530", "A112798", "A123528", "A123529", "A124010", "A240219", "A316413", "A326567", "A326568", "A326622", "A327473", "A327482", "A359903", "A359904", "A359905", "A359908", "A359913", "A360005", "A360008", "A360068" ]
null
Gus Wiseman, Jan 25 2023
2023-01-26T10:04:32
oeisdata/seq/A359/A359904.seq
494dca129fda5deb6d71616db6f4d81f
A359905
Numbers whose prime indices and prime signature both have integer mean.
[ "2", "3", "4", "5", "7", "8", "9", "10", "11", "13", "16", "17", "19", "21", "22", "23", "25", "27", "29", "30", "31", "32", "34", "37", "39", "41", "43", "46", "47", "49", "53", "55", "57", "59", "61", "62", "64", "67", "71", "73", "78", "79", "81", "82", "83", "85", "87", "88", "89", "91", "94", "97", "100", "101", "103", "105", "107", "109", "110", "111", "113", "115", "118", "121" ]
[ "nonn" ]
6
0
5
[ "A001222", "A008284", "A056239", "A058398", "A067340", "A088529", "A088530", "A112798", "A124010", "A316413", "A326567", "A326568", "A326622", "A327473", "A327482", "A328966", "A348551", "A359904", "A359905", "A359908", "A360005", "A360068", "A360069" ]
null
Gus Wiseman, Jan 25 2023
2023-01-26T10:04:28
oeisdata/seq/A359/A359905.seq
a54cd765034095d0a4b23806e6b5fd66
A359906
Number of integer partitions of n with integer mean and integer median.
[ "1", "2", "2", "4", "2", "8", "2", "10", "9", "14", "2", "39", "2", "24", "51", "49", "2", "109", "2", "170", "144", "69", "2", "455", "194", "116", "381", "668", "2", "1378", "2", "985", "956", "316", "2043", "4328", "2", "511", "2293", "6656", "2", "8634", "2", "8062", "14671", "1280", "2", "26228", "8035", "15991", "11614", "25055", "2", "47201", "39810", "65092" ]
[ "nonn" ]
6
0
5
[ "A000009", "A000016", "A000041", "A000975", "A008284", "A051293", "A058398", "A067538", "A082550", "A102627", "A237984", "A240219", "A316413", "A325347", "A326567", "A326568", "A326622", "A326669", "A327475", "A327482", "A328966", "A349156", "A359893", "A359894", "A359897", "A359901", "A359902", "A359905", "A359906", "A359907", "A359908", "A360005", "A360009" ]
null
Gus Wiseman, Jan 21 2023
2023-01-22T09:15:15
oeisdata/seq/A359/A359906.seq
2872177184174da1239ec3bb32d9f2f0
A359907
Number of strict integer partitions of n with integer median.
[ "0", "1", "1", "1", "2", "1", "4", "2", "6", "4", "9", "6", "14", "10", "18", "16", "27", "23", "36", "34", "51", "49", "67", "68", "94", "95", "122", "129", "166", "174", "217", "233", "287", "308", "371", "405", "487", "528", "622", "683", "805", "880", "1024", "1127", "1305", "1435", "1648", "1818", "2086", "2295", "2611", "2882", "3273", "3606", "4076", "4496", "5069" ]
[ "nonn" ]
6
0
5
[ "A000009", "A000016", "A000041", "A000975", "A005578", "A008284", "A051293", "A058398", "A067538", "A082550", "A102627", "A240219", "A240850", "A316413", "A325347", "A326567", "A326568", "A326669", "A327475", "A327482", "A328966", "A359893", "A359897", "A359901", "A359902", "A359907", "A359908", "A360005" ]
null
Gus Wiseman, Jan 21 2023
2023-01-22T09:14:59
oeisdata/seq/A359/A359907.seq
8cfb92beb0a3aa1d5821458ac2154914
A359908
Numbers whose prime indices have integer median.
[ "2", "3", "4", "5", "7", "8", "9", "10", "11", "12", "13", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "27", "28", "29", "30", "31", "32", "34", "37", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "52", "53", "54", "55", "56", "57", "59", "61", "62", "63", "64", "66", "67", "68", "70", "71", "72", "73", "75", "76", "78", "79", "80", "81", "82", "83" ]
[ "nonn" ]
5
0
5
[ "A001222", "A026424", "A027193", "A056239", "A112798", "A307683", "A316413", "A325347", "A359889", "A359890", "A359893", "A359901", "A359902", "A359903", "A359905", "A359907", "A359908", "A359912", "A360005", "A360006", "A360009" ]
null
Gus Wiseman, Jan 23 2023
2023-01-23T12:41:33
oeisdata/seq/A359/A359908.seq
97b9fdc04201c31bfb82c6ee3898414f
A359909
Number of integer factorizations of n into factors > 1 with the same mean as median.
[ "0", "1", "1", "2", "1", "2", "1", "3", "2", "2", "1", "3", "1", "2", "2", "4", "1", "3", "1", "3", "2", "2", "1", "5", "2", "2", "3", "3", "1", "4", "1", "4", "2", "2", "2", "6", "1", "2", "2", "4", "1", "4", "1", "3", "3", "2", "1", "6", "2", "3", "2", "3", "1", "4", "2", "4", "2", "2", "1", "7", "1", "2", "3", "7", "2", "4", "1", "3", "2", "4", "1", "7", "1", "2", "3", "3", "2", "4", "1", "6", "4", "2", "1", "6", "2", "2", "2", "4", "1", "6", "2", "3", "2", "2", "2", "6", "1", "3", "3", "6", "1", "4", "1", "4", "5", "2", "1", "6", "1", "4", "2", "5", "1", "4", "2", "3", "3", "2", "2", "11" ]
[ "nonn" ]
13
0
5
[ "A001055", "A008284", "A058398", "A240219", "A316313", "A326567", "A326568", "A326622", "A327482", "A328966", "A359889", "A359893", "A359894", "A359897", "A359901", "A359902", "A359906", "A359909", "A359910", "A359911", "A360005" ]
null
Gus Wiseman, Jan 24 2023
2025-01-20T09:07:46
oeisdata/seq/A359/A359909.seq
81c96ce1dfc7ae6eb036c31a7f643594
A359910
Number of odd-length integer factorizations of n into factors > 1 with the same mean as median.
[ "0", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3" ]
[ "nonn" ]
13
0
5
[ "A001055", "A240219", "A316313", "A326567", "A326568", "A326622", "A328966", "A359889", "A359891", "A359894", "A359895", "A359897", "A359902", "A359906", "A359909", "A359910", "A359911", "A360005" ]
null
Gus Wiseman, Jan 24 2023
2025-01-20T13:09:35
oeisdata/seq/A359/A359910.seq
2fee5d9d9b53a57d5ace8af2f270a6ee
A359911
Number of integer factorizations of n into factors > 1 without the same mean as median.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "2", "0", "0", "0", "1", "0", "1", "0", "3", "0", "0", "0", "3", "0", "0", "0", "3", "0", "1", "0", "1", "1", "0", "0", "6", "0", "1", "0", "1", "0", "3", "0", "3", "0", "0", "0", "4", "0", "0", "1", "4", "0", "1", "0", "1", "0", "1", "0", "9", "0", "0", "1", "1", "0", "1", "0", "6", "1", "0", "0", "5", "0", "0", "0", "3", "0", "5", "0", "1", "0", "0", "0", "13", "0", "1", "1", "3", "0", "1", "0", "3", "0", "0", "0", "10" ]
[ "nonn" ]
10
0
5
[ "A001055", "A240219", "A316313", "A326567", "A326568", "A326622", "A328966", "A359889", "A359894", "A359897", "A359906", "A359909", "A359910", "A359911", "A360005" ]
null
Gus Wiseman, Jan 24 2023
2025-01-20T10:40:53
oeisdata/seq/A359/A359911.seq
c69b2f74272ed02a0a9b7a42ed386ff2
A359912
Numbers whose prime indices do not have integer median.
[ "1", "6", "14", "15", "26", "33", "35", "36", "38", "51", "58", "60", "65", "69", "74", "77", "84", "86", "93", "95", "106", "119", "122", "123", "132", "141", "142", "143", "145", "150", "156", "158", "161", "177", "178", "185", "196", "201", "202", "204", "209", "210", "214", "215", "216", "217", "219", "221", "225", "226", "228", "249", "262", "265", "276", "278" ]
[ "nonn" ]
7
0
5
[ "A001222", "A026424", "A051293", "A056239", "A067538", "A072978", "A112798", "A175352", "A175761", "A289509", "A307683", "A316413", "A325347", "A326567", "A326568", "A326839", "A326840", "A348551", "A349156", "A359890", "A359893", "A359901", "A359902", "A359905", "A359907", "A359908", "A359912", "A359913", "A360005", "A360006", "A360009" ]
null
Gus Wiseman, Jan 24 2023
2023-01-25T09:09:04
oeisdata/seq/A359/A359912.seq
d17d68225a95f8d2238adb23dcf40b86
A359913
Numbers whose multiset of prime factors has integer median.
[ "2", "3", "4", "5", "7", "8", "9", "11", "12", "13", "15", "16", "17", "18", "19", "20", "21", "23", "24", "25", "27", "28", "29", "30", "31", "32", "33", "35", "37", "39", "40", "41", "42", "43", "44", "45", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "59", "61", "63", "64", "65", "66", "67", "68", "69", "70", "71", "72", "73", "75", "76", "77", "78", "79", "80", "81" ]
[ "nonn" ]
5
0
5
[ "A001222", "A027746", "A056239", "A067340", "A067538", "A072978", "A078175", "A112798", "A175352", "A316413", "A325347", "A326567", "A326568", "A326839", "A326840", "A348551", "A359890", "A359893", "A359901", "A359902", "A359905", "A359907", "A359908", "A359912", "A359913", "A360005", "A360006", "A360007", "A360069" ]
null
Gus Wiseman, Jan 25 2023
2023-01-26T10:04:19
oeisdata/seq/A359/A359913.seq
caae88dd551d88e2a725e53fd57ff4af
A359914
a(n) = coefficient of x^n in A(x) such that 2 = Sum_{n=-oo..+oo} (-1)^n * x^(n*(3*n-1)/2) * A(x)^(3*n) * (1 + x^n*A(x)).
[ "1", "2", "4", "30", "154", "1078", "7046", "50766", "364268", "2713444", "20384884", "155954760", "1204192106", "9400024042", "73945396990", "586088682472", "4673927031694", "37484566094970", "302098932029282", "2445538771089012", "19875632898821430", "162118004651048048", "1326658157736876148" ]
[ "nonn" ]
43
0
5
[ "A000041", "A040051", "A359914", "A359915", "A359916", "A359919", "A359920", "A359921", "A359924", "A361552" ]
null
Paul D. Hanna, Jan 23 2023
2024-01-19T10:06:08
oeisdata/seq/A359/A359914.seq
740bf52973c67a7f50fdb8437015ff33
A359915
a(n) = coefficient of x^n in A(x) such that A(x) = Sum_{n=-oo..+oo} (x*A(x))^(n*(3*n+1)/2) * (1/x^(3*n) - x^(3*n+1)).
[ "1", "1", "5", "23", "121", "713", "4487", "29374", "197896", "1363770", "9570226", "68156319", "491347930", "3578755113", "26295477075", "194677798065", "1450833583380", "10875262975274", "81940144475296", "620223662770067", "4714016885082577", "35962615212212852", "275282740190267268", "2113705107245941938" ]
[ "nonn" ]
17
0
5
[ "A359914", "A359915", "A359916", "A359919", "A359920", "A359921", "A359924" ]
null
Paul D. Hanna, Jan 22 2023
2024-01-05T17:17:31
oeisdata/seq/A359/A359915.seq
b295d07fef3a38897a856ff2b71f8ac2
A359916
a(n) = coefficient of x^n in A(x) such that A(x) = 1 + Sum_{n=-oo..+oo} x^(n*(3*n+1)/2) * (1/A(x)^(3*n) - A(x)^(3*n+1)).
[ "1", "1", "7", "48", "349", "2718", "22403", "192375", "1701544", "15389227", "141643233", "1322344998", "12491424723", "119177917679", "1146750961711", "11115577075944", "108437559699613", "1063849149587086", "10489551647580027", "103891138998923739", "1033113794091793406", "10310925888014393461" ]
[ "nonn" ]
15
0
5
[ "A359914", "A359915", "A359916", "A359919", "A359920", "A359921", "A359924" ]
null
Paul D. Hanna, Jan 22 2023
2024-01-05T16:36:25
oeisdata/seq/A359/A359916.seq
bb81e4d51143357696fd304f13762945
A359917
E.g.f.: lim_{N->oo} [ Sum_{n>=0} (N^2 + N*n + 2*n^2)^n * (x/N)^n/n! ]^(1/N).
[ "1", "1", "3", "28", "413", "9216", "268327", "9831424", "432251577", "22259307520", "1313366140331", "87431498993664", "6482838033725077", "529958491541291008", "47356678577690489295", "4592761099982656823296", "480465410003489098874993", "53933291626260492656050176", "6466413087139041540884403667" ]
[ "nonn" ]
13
0
5
[ "A266481", "A266485", "A318633", "A319147", "A319834", "A359917", "A359918", "A359927" ]
null
Paul D. Hanna, Jan 21 2023
2024-03-21T04:47:04
oeisdata/seq/A359/A359917.seq
e5bbe32a00ce32f29c789af241512a1d
A359918
a(n) = coefficient of x^n*y^(n+1)/n! in (1/2) * log( Sum_{n>=0} (n^2 + n*y + 2*y^2)^n * x^n/n! ).
[ "1", "2", "21", "304", "6985", "205056", "7607509", "337188608", "17495079921", "1038495001600", "69496455755221", "5176052539987968", "424783071501394489", "38087843235679268864", "3704990294840345047125", "388631778963216211050496", "43729459820175064700435041", "5254332451028464517449777152" ]
[ "nonn" ]
11
0
5
[ "A318634", "A319834", "A359917", "A359918", "A359926", "A359928" ]
null
Paul D. Hanna, Jan 21 2023
2024-03-21T04:54:39
oeisdata/seq/A359/A359918.seq
84b5ec0942be39ea8010ed32aba026d4
A359919
a(n) = coefficient of x^n in A(x) such that x^2 = Sum_{n=-oo..+oo} x^(n*(3*n+1)/2) * (A(x)^(3*n) - 1/A(x)^(3*n+1)).
[ "1", "0", "1", "5", "19", "65", "211", "681", "2255", "7830", "28786", "111230", "443789", "1795972", "7284981", "29466755", "118834438", "479034654", "1936617163", "7872885832", "32226147305", "132808096158", "550444192577", "2291095125465", "9564074472264", "40005894288101", "167610376198140", "703308153554903" ]
[ "nonn" ]
16
0
5
[ "A359914", "A359915", "A359916", "A359919", "A359920", "A359921", "A359924" ]
null
Paul D. Hanna, Jan 22 2023
2024-01-05T17:17:35
oeisdata/seq/A359/A359919.seq
e5f52e9824f7573fa99ae16eae9e8aaf
A359920
a(n) = coefficient of x^n in A(x) such that x = Sum_{n=-oo..+oo} x^(n*(3*n+1)/2) * (A(x)^(3*n) - 1/A(x)^(3*n+1)).
[ "1", "1", "6", "29", "137", "690", "3815", "22579", "138353", "862692", "5451339", "34911444", "226475135", "1485571965", "9833401534", "65578882177", "440170565711", "2971402946711", "20161828468803", "137434420403678", "940701180157773", "6462787501335564", "44550102080595910", "308041365014677804", "2135938633975050831" ]
[ "nonn" ]
35
0
5
[ "A359719", "A359914", "A359915", "A359916", "A359919", "A359920", "A359921", "A359924" ]
null
Paul D. Hanna, Jan 22 2023
2024-01-19T09:03:17
oeisdata/seq/A359/A359920.seq
0cafa470ccba3cf6e79cbf7c946bcb66
A359921
a(n) = coefficient of x^n in A(x) such that 1/x = Sum_{n=-oo..+oo} x^(n*(3*n+1)/2) * (A(x)^(3*n) - 1/A(x)^(3*n+1)).
[ "1", "1", "9", "80", "774", "8077", "89059", "1021106", "12048985", "145347965", "1784282449", "22217589408", "279934808090", "3562376922346", "45721210139842", "591139659619262", "7692224199601436", "100663182977093130", "1323944771879772911", "17491108974090887920", "232015023433972687373", "3088855705228007528177" ]
[ "nonn" ]
23
0
5
[ "A359920", "A359921", "A359924", "A361050", "A361052", "A361538" ]
null
Paul D. Hanna, Jan 22 2023
2024-01-05T16:37:40
oeisdata/seq/A359/A359921.seq
a6363083fb355d8b8244fae6fff86ba1
A359922
a(n) = coefficient of x^n in A(x) where x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^n * (2 + x^n*A(x)^n)^n.
[ "1", "1", "4", "9", "42", "187", "775", "3470", "16085", "76521", "368274", "1791494", "8829531", "43964379", "220667042", "1115235384", "5671532510", "29004157940", "149056379047", "769368598912", "3986831368824", "20733495321171", "108175116519808", "566067951728994", "2970221822319878", "15624080964153005" ]
[ "nonn" ]
7
0
5
[ "A359672", "A359922", "A359923" ]
null
Paul D. Hanna, Jan 18 2023
2023-01-21T18:44:05
oeisdata/seq/A359/A359922.seq
c5f27ac7eb8d2f4280b2de1420c0afb9
A359923
a(n) = coefficient of x^n in A(x) where x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^n * (3 + x^n*A(x)^n)^n.
[ "1", "1", "6", "15", "69", "376", "1741", "8860", "46044", "245074", "1336538", "7337135", "40736876", "228625148", "1293530435", "7372491383", "42275811853", "243742895280", "1412310750812", "8219298313118", "48023377286364", "281592177442072", "1656522460985914", "9773791391488278", "57824226906859849" ]
[ "nonn" ]
9
0
5
[ "A359672", "A359922", "A359923" ]
null
Paul D. Hanna, Jan 18 2023
2023-01-21T18:44:32
oeisdata/seq/A359/A359923.seq
9880f91685b305cdadda8e50edf2e440
A359924
a(n) = coefficient of x^n in A(x) such that 2/x = Sum_{n=-oo..+oo} x^(n*(3*n+1)/2) * (A(x)^(3*n) - 1/A(x)^(3*n+1)).
[ "1", "2", "26", "372", "6006", "105338", "1952102", "37598422", "745116966", "15094772444", "311183832004", "6507065710068", "137683172641240", "2942394474649322", "63418690179207242", "1376986195691108990", "30090726682472126472", "661292884776232386766", "14606177871231796042658", "324062328994910188622258" ]
[ "nonn" ]
21
0
5
[ "A359920", "A359921", "A359924", "A361050", "A361052", "A361538" ]
null
Paul D. Hanna, Jan 22 2023
2024-01-05T17:17:39
oeisdata/seq/A359/A359924.seq
be794fb9b11f88c341bcab8ac9ce6a71
A359925
Numbers with easy multiplication table - the first 9 multiples of these numbers can be derived by either incrementing or decrementing the corresponding digits from the previous multiple.
[ "1", "9", "11", "89", "91", "109", "111", "889", "891", "909", "911", "1089", "1091", "1109", "1111", "8889", "8891", "8909", "8911", "9089", "9091", "9109", "9111", "10889", "10891", "10909", "10911", "11089", "11091", "11109", "11111", "88889", "88891", "88909", "88911", "89089", "89091", "89109", "89111", "90889", "90891", "90909", "90911" ]
[ "nonn", "base" ]
46
0
5
[ "A006257", "A147991", "A147992", "A147993", "A153777", "A256290", "A359925", "A360099" ]
null
Kiran Ananthpur Bacche, Jan 25 2023
2023-01-30T18:49:55
oeisdata/seq/A359/A359925.seq
3bc31661658c53459e46545e8b88b69b
A359926
a(n) = coefficient of x^n*y^(n+1)/n! in (1/4) * log( Sum_{n>=0} (n + 2*y)^(2*n) * x^n/n! ).
[ "1", "8", "168", "6016", "309760", "20957184", "1762991104", "177690607616", "20895204704256", "2810343286374400", "425698411965054976", "71735043897868419072", "13313460758336789020672", "2698754565131159025483776", "593332971403056575938560000", "140634107346363806457259884544" ]
[ "nonn" ]
18
0
5
[ "A266485", "A318634", "A319834", "A359926", "A359928" ]
null
Paul D. Hanna, Jan 20 2023
2024-03-17T06:40:20
oeisdata/seq/A359/A359926.seq
c58d2212008cb397fa4d69c297a0a6b2
A359927
E.g.f.: lim_{N->oo} [ Sum_{n>=0} (N^2 + 3*N*n + 2*n^2)^n * (x/N)^n/n! ]^(1/N).
[ "1", "1", "7", "112", "2965", "111856", "5528419", "339433984", "24965493865", "2142654088960", "210377086601311", "23269631260880896", "2864038963868253373", "388330717110688399360", "57521524729462484086075", "9242821569458332441378816", "1601434996324769244061560529" ]
[ "nonn" ]
17
0
5
[ "A266481", "A318633", "A319147", "A359927", "A359928" ]
null
Paul D. Hanna, Jan 20 2023
2023-03-14T04:34:02
oeisdata/seq/A359/A359927.seq
2dd09375e858caec0bcd30dcc22db3d3
A359928
a(n) = coefficient of x^n*y^(n+1)/n! in (1/2) * log( Sum_{n>=0} (n^2 + 3*n*y + 2*y^2)^n * x^n/n! ).
[ "1", "6", "93", "2448", "92505", "4589568", "283008621", "20903023872", "1800986581521", "177455695795200", "19690717755237309", "2430478269127673856", "330392930155527272553", "49053029845102480576512", "7898602773992589665290125", "1371137549213022697047785472", "255275516636592894833768588961" ]
[ "nonn" ]
13
0
5
[ "A318634", "A319834", "A359927", "A359928" ]
null
Paul D. Hanna, Jan 20 2023
2024-03-21T04:59:19
oeisdata/seq/A359/A359928.seq
1580dccf6be1bdf9f90643916743acba
A359929
Irregular triangle read by rows, where row n lists k < t such that rad(k) = rad(t) but k does not divide t, where t = A360768(n) and rad(k) = A007947(k).
[ "12", "18", "24", "18", "36", "20", "40", "12", "24", "36", "48", "48", "54", "45", "50", "60", "18", "36", "54", "72", "28", "56", "40", "80", "24", "48", "72", "96", "98", "90", "84", "75", "54", "96", "108", "63", "60", "90", "120", "50", "100", "12", "24", "36", "48", "72", "96", "108", "144", "126", "120", "150", "147", "18", "36", "54", "72", "108", "144", "162", "56", "112", "132", "80", "160", "48", "96", "144", "162", "192", "98", "196" ]
[ "nonn", "tabf" ]
10
0
5
[ "A007947", "A126706", "A355432", "A359382", "A359929", "A360768" ]
null
Michael De Vlieger, Mar 29 2023
2023-04-01T13:29:05
oeisdata/seq/A359/A359929.seq
b8deae84245ed41adce2bb25140897d9
A359930
The number of practical numbers strictly between A005153(n) and A005153(n)^(1+1/n).
[ "0", "0", "1", "1", "1", "2", "2", "2", "1", "3", "3", "2", "2", "2", "2", "1", "3", "4", "3", "3", "3", "2", "3", "4", "3", "3", "3", "3", "4", "3", "3", "2", "3", "3", "4", "3", "3", "3", "4", "4", "4", "4", "3", "2", "3", "4", "6", "6", "6", "5", "5", "5", "4", "4", "4", "3", "2", "3", "3", "6", "6", "5", "5", "5", "4", "4", "4", "6", "5", "6", "5", "5", "4", "4", "5", "5", "5", "5", "5", "4", "4", "4", "5", "5", "5", "6" ]
[ "nonn" ]
10
0
5
[ "A005153", "A182134", "A359930" ]
null
Hal M. Switkay, Jan 18 2023
2023-01-29T10:45:31
oeisdata/seq/A359/A359930.seq
5011604ff6434890f73d9cc0e104817f
A359931
Number of distinct circles that can be constructed from an n x n square grid of points using only a compass.
[ "8", "38", "120", "277", "544", "969", "1616", "2494", "3724", "5331", "7408", "10038", "13284", "17181", "21968", "27653", "34320", "42110", "51148" ]
[ "nonn", "more" ]
5
0
5
[ "A359931", "A359932", "A359933", "A359934", "A359935" ]
null
Scott R. Shannon, Jan 19 2023
2023-01-22T08:58:19
oeisdata/seq/A359/A359931.seq
24c45c1c16385b55264618a6f1fb3bef
A359932
Number of vertices among all distinct circles that can be constructed from an n x n square grid of points using only a compass.
[ "40", "689", "7240", "38729", "151584", "488741" ]
[ "nonn", "more" ]
10
0
5
[ "A359252", "A359859", "A359931", "A359932", "A359933", "A359934", "A359935" ]
null
Scott R. Shannon, Jan 19 2023
2023-01-22T08:58:55
oeisdata/seq/A359/A359932.seq
1573e534382fa176f53c06f0e5f968bb
A359933
Number of regions among all distinct circles that can be constructed from an n X n square grid of points using only a compass.
[ "45", "836", "8197", "43252", "167157", "535572" ]
[ "nonn", "more" ]
16
0
5
[ "A359253", "A359860", "A359931", "A359932", "A359933", "A359934", "A359935" ]
null
Scott R. Shannon, Jan 21 2023
2023-04-13T02:35:20
oeisdata/seq/A359/A359933.seq
ccac23729dcf4a624cab7c446f38ea6b
A359934
Number of edges among all distinct circles that can be constructed from an n x n square grid of points using only a compass.
[ "84", "1524", "15436", "81980", "318740", "1024312" ]
[ "nonn", "more" ]
7
0
5
[ "A359254", "A359861", "A359931", "A359932", "A359933", "A359934", "A359935" ]
null
Scott R. Shannon, Jan 21 2023
2023-01-22T08:59:14
oeisdata/seq/A359/A359934.seq
4c68a443f417a69eb07dd33caaf06500
A359935
Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, among all distinct circles that can be constructed from an n x n square grid of points using only a compass.
[ "0", "16", "30", "0", "412", "341", "60", "20", "4", "0", "3464", "3534", "928", "212", "48", "12", "0", "16936", "19861", "5252", "1056", "88", "52", "8", "0", "63712", "77394", "20480", "4820", "612", "108", "20", "12", "4", "202904", "244013", "71244", "14968", "1852", "472", "80", "32", "4" ]
[ "nonn", "tabf", "more" ]
12
0
5
[ "A359258", "A359862", "A359931", "A359932", "A359933", "A359934", "A359935" ]
null
Scott R. Shannon, Jan 21 2023
2024-01-04T14:45:51
oeisdata/seq/A359/A359935.seq
1cffa3e0c68edcc75b15ca80fceb2b8a
A359936
Expansion of Product_{k>=0} (1 - x^(k^2+1)) in powers of x.
[ "1", "-1", "-1", "1", "0", "-1", "1", "1", "-1", "0", "-1", "1", "1", "-1", "0", "1", "-1", "-2", "2", "1", "-1", "0", "1", "-1", "-1", "1", "-1", "2", "0", "-2", "1", "1", "-2", "0", "2", "-1", "1", "-2", "0", "2", "-1", "-1", "2", "1", "-3", "0", "1", "1", "-2", "0", "1", "0", "0", "-1", "3", "0", "-3", "0", "2", "-2", "1", "1", "-2", "2", "-2", "-2", "4", "2", "-4", "1", "2", "-3", "-1", "1", "2", "1", "-1", "-3", "2" ]
[ "sign", "look" ]
14
0
5
[ "A002522", "A081362", "A276516", "A284312", "A284313", "A284314", "A284499", "A284585", "A357911", "A359936", "A359937" ]
null
Seiichi Manyama, Jan 19 2023
2023-01-19T09:34:32
oeisdata/seq/A359/A359936.seq
334d8ef23eecaa15c39668d24db3b263
A359937
a(n) = Sum_{d|n, d-1 is square} d.
[ "1", "3", "1", "3", "6", "3", "1", "3", "1", "18", "1", "3", "1", "3", "6", "3", "18", "3", "1", "18", "1", "3", "1", "3", "6", "29", "1", "3", "1", "18", "1", "3", "1", "20", "6", "3", "38", "3", "1", "18", "1", "3", "1", "3", "6", "3", "1", "3", "1", "68", "18", "29", "1", "3", "6", "3", "1", "3", "1", "18", "1", "3", "1", "3", "71", "3", "1", "20", "1", "18", "1", "3", "1", "40", "6", "3", "1", "29", "1", "18", "1", "85", "1", "3" ]
[ "nonn" ]
18
0
5
[ "A002522", "A035316", "A359937", "A359967" ]
null
Seiichi Manyama, Jan 19 2023
2023-01-21T03:31:00
oeisdata/seq/A359/A359937.seq
ced93709881db5bfe611c77a7dbd78cf
A359938
Number of divisors d of n such that d-1 is square.
[ "1", "2", "1", "2", "2", "2", "1", "2", "1", "4", "1", "2", "1", "2", "2", "2", "2", "2", "1", "4", "1", "2", "1", "2", "2", "3", "1", "2", "1", "4", "1", "2", "1", "3", "2", "2", "2", "2", "1", "4", "1", "2", "1", "2", "2", "2", "1", "2", "1", "5", "2", "3", "1", "2", "2", "2", "1", "2", "1", "4", "1", "2", "1", "2", "3", "2", "1", "3", "1", "4", "1", "2", "1", "3", "2", "2", "1", "3", "1", "4", "1", "3", "1", "2", "3", "2", "1", "2", "1", "4" ]
[ "nonn" ]
30
0
5
[ "A002522", "A046951", "A113319", "A359937", "A359938", "A359944" ]
null
Seiichi Manyama, Jan 19 2023
2024-08-18T20:48:39
oeisdata/seq/A359/A359938.seq
d0055d900b4163c639add8d25e4fbe39
A359939
Lexicographically earliest strictly increasing sequence of primes whose partial products lie between noncomposite numbers.
[ "2", "3", "5", "19", "41", "67", "113", "653", "883", "1439", "3823", "10631", "12841", "14251", "23357", "27103", "30491", "64679", "78823", "110977", "115127", "118747", "159431", "215587", "301039", "342257", "343639", "428401", "473383", "493583", "566723", "621133", "638371", "639157", "680539", "904049", "993037", "1146133", "1252507" ]
[ "nonn" ]
10
0
5
[ "A008578", "A014574", "A039726", "A087898", "A167777", "A359939", "A359940" ]
null
Amiram Eldar, Jan 19 2023
2023-01-21T03:27:42
oeisdata/seq/A359/A359939.seq
f6f46470df63aa8d9debaaa06967d55d
A359940
Lexicographically earliest sequence of distinct primes whose partial products lie between noncomposite numbers.
[ "2", "3", "5", "19", "11", "7", "31", "23", "193", "67", "367", "131", "317", "1097", "241", "1777", "773", "2819", "2689", "1381", "1741", "3389", "631", "8581", "41", "1553", "2297", "1427", "17053", "1493", "883", "619", "9803", "13331", "26203", "37", "7681", "41269", "1913", "27091", "3079", "31583", "5867", "22409", "13367", "37337", "29573", "6469" ]
[ "nonn" ]
12
0
5
[ "A008578", "A014574", "A083771", "A167777", "A290427", "A359939", "A359940" ]
null
Amiram Eldar, Jan 19 2023
2023-01-21T03:27:38
oeisdata/seq/A359/A359940.seq
e3835f6ba1df4961d21c227932b3da6c
A359941
Irregular triangle read row by row. The k-th row are integers from 0 to 2^k-1 in base 2 ordered in graded reverse lexicographical order.
[ "0", "0", "1", "0", "1", "2", "3", "0", "1", "2", "4", "3", "5", "6", "7", "0", "1", "2", "4", "8", "3", "5", "9", "6", "10", "12", "7", "11", "13", "14", "15", "0", "1", "2", "4", "8", "16", "3", "5", "9", "17", "6", "10", "18", "12", "20", "24", "7", "11", "19", "13", "21", "25", "14", "22", "26", "28", "15", "23", "27", "29", "30", "31", "0", "1", "2", "4", "8", "16", "32", "3", "5", "9", "17", "33", "6" ]
[ "nonn", "base", "look", "tabf", "easy" ]
24
0
5
[ "A023443", "A082185", "A359941", "A360302" ]
null
Jean Liénardy, Jan 19 2023
2023-02-18T10:37:48
oeisdata/seq/A359/A359941.seq
0e962bc15604e311529909c127c8d184
A359942
Expansion of Product_{k>=0} (1 - x^(k^3+1)) in powers of x.
[ "1", "-1", "-1", "1", "0", "0", "0", "0", "0", "-1", "1", "1", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "1", "1", "-1", "0", "0", "0", "0", "0", "1", "-1", "-1", "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", "-1", "1", "1", "-1", "0", "0", "0", "0", "0", "1", "-1", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
11
0
5
[ "A001093", "A279484", "A359936", "A359942", "A359943" ]
null
Seiichi Manyama, Jan 19 2023
2023-01-19T11:04:22
oeisdata/seq/A359/A359942.seq
82440e7048fa8cec315f3d36a62db2b0
A359943
a(n) = Sum_{d|n, d-1 is cube} d.
[ "1", "3", "1", "3", "1", "3", "1", "3", "10", "3", "1", "3", "1", "3", "1", "3", "1", "12", "1", "3", "1", "3", "1", "3", "1", "3", "10", "31", "1", "3", "1", "3", "1", "3", "1", "12", "1", "3", "1", "3", "1", "3", "1", "3", "10", "3", "1", "3", "1", "3", "1", "3", "1", "12", "1", "31", "1", "3", "1", "3", "1", "3", "10", "3", "66", "3", "1", "3", "1", "3", "1", "12", "1", "3", "1", "3", "1", "3", "1", "3", "10", "3", "1", "31", "1", "3" ]
[ "nonn" ]
11
0
5
[ "A001093", "A113061", "A359937", "A359942", "A359943", "A359944" ]
null
Seiichi Manyama, Jan 19 2023
2023-08-09T00:52:52
oeisdata/seq/A359/A359943.seq
992f7f5565dda4e3b43a59c515689d18
A359944
Number of divisors d of n such that d-1 is a cube.
[ "1", "2", "1", "2", "1", "2", "1", "2", "2", "2", "1", "2", "1", "2", "1", "2", "1", "3", "1", "2", "1", "2", "1", "2", "1", "2", "2", "3", "1", "2", "1", "2", "1", "2", "1", "3", "1", "2", "1", "2", "1", "2", "1", "2", "2", "2", "1", "2", "1", "2", "1", "2", "1", "3", "1", "3", "1", "2", "1", "2", "1", "2", "2", "2", "2", "2", "1", "2", "1", "2", "1", "3", "1", "2", "1", "2", "1", "2", "1", "2", "2", "2", "1", "3", "1", "2", "1", "2", "1", "3", "1" ]
[ "nonn" ]
24
0
5
[ "A001093", "A061704", "A339606", "A359944" ]
null
Seiichi Manyama, Jan 19 2023
2024-08-18T20:48:58
oeisdata/seq/A359/A359944.seq
745e35c896eb1259fe36bd9bd6f8927a
A359945
Largest k < n such that n! / k! = m! = A000142(m) for some m.
[ "0", "1", "1", "1", "1", "5", "1", "1", "1", "7", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "23", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn" ]
18
0
5
[ "A000142", "A003135", "A359945" ]
null
M. F. Hasler, Jan 19 2023
2023-01-31T08:54:19
oeisdata/seq/A359/A359945.seq
99e9c16ddd2d9c0c3b7f27212e027f1c
A359946
Lexicographically earliest sequence of distinct positive integers such that for any n > 0, n XOR a(n) is a prime number (where XOR denotes the bitwise XOR operator).
[ "2", "1", "4", "3", "6", "5", "10", "11", "12", "7", "8", "9", "14", "13", "16", "15", "18", "17", "20", "19", "22", "21", "26", "27", "28", "23", "24", "25", "30", "29", "34", "35", "36", "31", "32", "33", "38", "37", "42", "43", "44", "39", "40", "41", "46", "45", "48", "47", "50", "49", "52", "51", "54", "53", "58", "59", "60", "55", "56", "57", "62", "61", "64", "63", "66", "65", "68" ]
[ "nonn", "base" ]
6
0
5
[ "A004443", "A359946", "A359947" ]
null
Rémy Sigrist, Jan 19 2023
2023-01-21T16:25:10
oeisdata/seq/A359/A359946.seq
0aeae7e92ec80b6a7115c05ca7e5f659
A359947
a(n) = n XOR A359946(n) (where XOR denotes the bitwise XOR operator).
[ "3", "3", "7", "7", "3", "3", "13", "3", "5", "13", "3", "5", "3", "3", "31", "31", "3", "3", "7", "7", "3", "3", "13", "3", "5", "13", "3", "5", "3", "3", "61", "3", "5", "61", "3", "5", "3", "3", "13", "3", "5", "13", "3", "5", "3", "3", "31", "31", "3", "3", "7", "7", "3", "3", "13", "3", "5", "13", "3", "5", "3", "3", "127", "127", "3", "3", "7", "7", "3", "3", "13", "3", "5", "13", "3", "5", "3", "3", "31", "31" ]
[ "nonn", "base" ]
7
0
5
[ "A359946", "A359947" ]
null
Rémy Sigrist, Jan 19 2023
2023-01-22T03:01:30
oeisdata/seq/A359/A359947.seq
628cc24c18e0e8da379731c04a214ef8
A359948
Lexicographically earliest sequence of primes whose partial products lie between noncomposite numbers.
[ "2", "2", "3", "5", "3", "13", "5", "7", "41", "13", "83", "109", "347", "337", "127", "67", "379", "499", "739", "4243", "2311", "1973", "5827", "7333", "971", "3449", "3967", "3407", "12671", "1423", "859", "20641", "7237", "769", "9209", "281", "12919", "16633", "11383", "30449", "6733", "40627", "34591", "1103", "14303", "5479", "4603", "17477", "5113", "51001", "36299", "57037", "1153", "34297", "1237" ]
[ "nonn" ]
20
0
5
[ "A036014", "A359940", "A359948" ]
null
Robert Israel, Jan 19 2023
2023-07-08T10:42:28
oeisdata/seq/A359/A359948.seq
2208406bbfaec7ba19edfc9ffe53240e
A359949
Multiplicative sequence with a(p) = 3*p-1 and a(p^e) = (3*e*(p-1) + 3) * p^(e-1) for e > 1 and prime p.
[ "1", "5", "8", "18", "14", "40", "20", "48", "45", "70", "32", "144", "38", "100", "112", "120", "50", "225", "56", "252", "160", "160", "68", "384", "135", "190", "189", "360", "86", "560", "92", "288", "256", "250", "280", "810", "110", "280", "304", "672", "122", "800", "128", "576", "630", "340", "140", "960", "273", "675", "400", "684", "158", "945", "448", "960", "448", "430", "176", "2016" ]
[ "nonn", "easy", "mult" ]
9
0
5
[ "A000010", "A073184", "A359949" ]
null
Werner Schulte, Jan 19 2023
2023-02-07T15:12:41
oeisdata/seq/A359/A359949.seq
69d58e291eeb42113947542bb0005224
A359950
a(n) is the greatest prime factor of n^n - n!.
[ "2", "7", "29", "601", "29", "116929", "11887", "4778489", "82207", "296987", "2767", "464089", "36922117", "71722471217", "10219277051", "9406703479", "2040247819", "122450719", "1265072927", "18353142818474353", "21514105057", "46999724987", "29693667067", "5684341885088084044195811037649", "692132186353", "12114317049616531" ]
[ "nonn" ]
32
0
5
[ "A006530", "A020639", "A036679", "A126130", "A359950" ]
null
Sebastian F. Orellana, Jan 19 2023
2023-03-13T02:54:32
oeisdata/seq/A359/A359950.seq
5628e2d173270bb47570b1ad5a804b49
A359951
Number of permutations of [n] such that the GCD of the cycle lengths is a prime.
[ "0", "0", "1", "2", "3", "24", "145", "720", "4725", "22400", "602721", "3628800", "67692625", "479001600", "12924021825", "103953833984", "2116670180625", "20922789888000", "959231402754625", "6402373705728000", "257071215652932681", "3242340687872000000", "142597230222616430625", "1124000727777607680000" ]
[ "nonn" ]
17
0
5
[ "A000040", "A000142", "A005225", "A079128", "A214003", "A346085", "A346086", "A359951" ]
null
Alois P. Heinz, Jan 19 2023
2023-12-13T11:35:30
oeisdata/seq/A359/A359951.seq
b7ebdcdbf65e815fe85b8137a2f0ff79
A359952
Wieferich sequence where a(1) = 2.
[ "2", "1093", "5", "20771", "18043", "5", "20771", "18043", "5", "20771", "18043", "5", "20771", "18043", "5", "20771", "18043", "5", "20771", "18043", "5", "20771", "18043", "5", "20771", "18043", "5", "20771", "18043", "5", "20771", "18043", "5", "20771", "18043", "5", "20771", "18043", "5", "20771", "18043", "5", "20771", "18043" ]
[ "nonn" ]
15
0
5
[ "A178871", "A179400", "A179678", "A244550", "A297846", "A359952" ]
null
Robert C. Lyons, Jan 19 2023
2023-01-28T11:30:28
oeisdata/seq/A359/A359952.seq
be7442d9b5f16c81dafddb7e6718a044
A359953
a(1) = 0, a(2) = 1. For n >= 3, if the greatest prime dividing n is greater than the greatest prime dividing n-1, then a(n) = a(n-1) + 1. Otherwise a(n) = a(n-1) - 1.
[ "0", "1", "2", "1", "2", "1", "2", "1", "2", "3", "4", "3", "4", "3", "2", "1", "2", "1", "2", "1", "2", "3", "4", "3", "4", "5", "4", "5", "6", "5", "6", "5", "6", "7", "6", "5", "6", "5", "4", "3", "4", "3", "4", "3", "2", "3", "4", "3", "4", "3", "4", "3", "4", "3", "4", "3", "4", "5", "6", "5", "6", "5", "4", "3", "4", "3", "4", "3", "4", "3", "4", "3", "4", "3", "2", "3", "2", "3", "4", "3", "2", "3", "4", "3" ]
[ "easy", "sign" ]
26
0
5
[ "A000040", "A006530", "A070089", "A087429", "A359953" ]
null
Tamas Sandor Nagy, Jan 19 2023
2023-03-14T10:06:10
oeisdata/seq/A359/A359953.seq
695ffeaf997bdba45824f05d7c2cba79
A359954
a(n) = Sum_{d|n} tau(d)*phi(d)*mu(n/d).
[ "1", "1", "3", "4", "7", "3", "11", "10", "14", "7", "19", "12", "23", "11", "21", "24", "31", "14", "35", "28", "33", "19", "43", "30", "52", "23", "54", "44", "55", "21", "59", "56", "57", "31", "77", "56", "71", "35", "69", "70", "79", "33", "83", "76", "98", "43", "91", "72", "114", "52", "93", "92", "103", "54", "133", "110", "105", "55", "115", "84", "119", "59", "154", "128", "161", "57", "131" ]
[ "nonn", "easy", "mult" ]
26
0
5
[ "A000005", "A000010", "A008683", "A062355", "A359954", "A363012" ]
null
Wesley Ivan Hurt, May 12 2023
2023-05-17T11:13:25
oeisdata/seq/A359/A359954.seq
ec1b5306101f5848334618a1d392e72d
A359955
a(n) is the smallest number with exactly n divisors that are greater than or equal to 4.
[ "4", "8", "12", "20", "24", "36", "48", "80", "60", "140", "192", "144", "120", "280", "180", "700", "240", "560", "1600", "5120", "360", "1120", "10000", "900", "960", "2240", "720", "2800", "840", "3080", "25600", "5184", "1260", "5600", "175175", "36864", "1680", "6160", "2880", "11200", "15360", "3600", "19600", "3705625", "2520", "12320", "6480", "70000" ]
[ "nonn" ]
7
0
5
[ "A005179", "A321014", "A359955", "A359956", "A359957" ]
null
Ilya Gutkovskiy, Jan 19 2023
2023-01-28T12:39:48
oeisdata/seq/A359/A359955.seq
2d0e04f87e82f8aae5425e36c3dd8457
A359956
a(n) is the smallest number with exactly n divisors that are greater than or equal to 5.
[ "5", "10", "18", "24", "30", "48", "80", "60", "90", "192", "144", "120", "210", "180", "450", "240", "560", "1600", "5120", "360", "630", "3465", "900", "960", "2240", "720", "2800", "840", "1890", "10010", "5184", "1260", "3150", "17325", "36864", "1680", "5670", "2880", "11200", "15360", "3600", "19600", "99225", "2520", "6930", "6480", "70000", "61440" ]
[ "nonn" ]
9
0
5
[ "A005179", "A338648", "A359955", "A359956", "A359957" ]
null
Ilya Gutkovskiy, Jan 19 2023
2024-08-18T12:22:37
oeisdata/seq/A359/A359956.seq
94c6cd05664ed88c82e4380917c0b2d7
A359957
a(n) is the smallest number with exactly n divisors that are greater than or equal to 6.
[ "6", "12", "18", "24", "36", "48", "60", "72", "126", "192", "120", "168", "180", "252", "240", "336", "576", "3072", "360", "504", "1296", "900", "960", "1344", "720", "1008", "840", "1512", "4158", "27027", "1260", "2016", "9702", "63063", "1680", "3024", "2880", "4032", "15360", "3600", "7056", "94864", "2520", "5544", "6480", "9072", "61440", "86016" ]
[ "nonn" ]
9
0
5
[ "A005179", "A338649", "A359955", "A359956", "A359957" ]
null
Ilya Gutkovskiy, Jan 19 2023
2024-01-04T14:01:44
oeisdata/seq/A359/A359957.seq
0d1285c51aeddb382156c20843a5249f
A359958
a(n) is the smallest number with exactly n divisors that are greater than or equal to n.
[ "1", "4", "15", "20", "30", "48", "72", "160", "120", "210", "252", "240", "560", "360", "480", "864", "900", "720", "1200", "840", "1512", "1440", "1800", "2400", "2160", "3024", "2880", "4032", "3600", "2520", "3960", "5280", "6480", "9072", "14256", "6720", "8640", "5040", "12480", "7920", "7560", "9240", "11880", "16632", "20790", "10080", "12600", "15840" ]
[ "nonn" ]
6
0
5
[ "A005179", "A359955", "A359956", "A359957", "A359958" ]
null
Ilya Gutkovskiy, Jan 19 2023
2023-01-28T12:40:25
oeisdata/seq/A359/A359958.seq
6400de4177e40451726992fcedb4d261
A359959
a(n) is the least number that has exactly n divisors with the same digit sum.
[ "1", "10", "36", "54", "144", "108", "486", "216", "324", "432", "648", "540", "1296", "3510", "2430", "1080", "2700", "1620", "8424", "2160", "4860", "4320", "3240", "27216", "7560", "8100", "6480", "35100", "10800", "19440", "24300", "21060", "15120", "16200", "37800", "56700", "54000", "30240", "42120", "60480", "32400", "45360", "84240", "81000", "64800", "75600", "90720", "213840" ]
[ "nonn", "base" ]
16
0
5
[ "A007953", "A359074", "A359959" ]
null
Robert Israel, Jan 19 2023
2023-01-29T02:32:50
oeisdata/seq/A359/A359959.seq
4872020035818465c3c6b60798c2b4ec
A359960
Smallest Niven (or Harshad) number (A005349) with exactly n distinct prime factors.
[ "1", "2", "6", "30", "210", "2310", "30030", "690690", "14804790", "223092870", "8254436190", "200560490130", "8222980095330", "304250263527210", "13082761331670030", "614889782588491410", "32589158477190044730", "1987938667108592728530", "117288381359406970983270", "7858321551080267055879090" ]
[ "nonn", "base" ]
33
0
5
[ "A001221", "A002110", "A005349", "A060319", "A083002", "A113315", "A359960", "A359961", "A360011" ]
null
Bernard Schott, Jan 20 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359960.seq
9f96a0fc115df8ff5ab31182cfe7e506
A359961
Smallest Zuckerman number (A007602) with exactly n distinct prime factors.
[ "1", "2", "6", "132", "3276", "27132", "1117116", "111914712", "6111417312", "1113117121116", "1112712811322112", "11171121131111172" ]
[ "nonn", "base", "more" ]
21
0
5
[ "A007602", "A060319", "A083002", "A288069", "A359960", "A359961" ]
null
Bernard Schott, Jan 21 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359961.seq
713334153b51270eb694b9f35c0bf289
A359962
Number of multisets of n nonempty words with a total of 2n letters over binary alphabet.
[ "1", "4", "26", "132", "623", "2632", "10500", "39384", "141659", "490100", "1644186", "5366436", "17113433", "53454528", "163963312", "494786352", "1471423866", "4318092136", "12520027756", "35901819336", "101909674398", "286575107424", "798886300056", "2209115439664", "6062818714752", "16522049256656" ]
[ "nonn" ]
26
0
5
[ "A209406", "A359962", "A360626" ]
null
Alois P. Heinz, Jan 20 2023
2023-02-14T12:31:06
oeisdata/seq/A359/A359962.seq
6524796f77927b10b57142c8e43dde23
A359963
Arithmetic numbers (A003601) having more divisors than all smaller arithmetic numbers.
[ "1", "3", "6", "20", "30", "60", "168", "420", "840", "1980", "2160", "2520", "7560", "10080", "15120", "27720", "79200", "83160", "110880", "166320", "262080", "332640", "554400", "786240", "831600", "1081080", "1441440", "2162160", "2882880", "4324320", "7207200", "8648640", "10810800", "17297280", "21621600", "36756720", "43243200" ]
[ "nonn" ]
13
0
5
[ "A000005", "A002182", "A003601", "A335317", "A359963", "A359964", "A359965" ]
null
Amiram Eldar, Jan 20 2023
2023-01-23T02:33:13
oeisdata/seq/A359/A359963.seq
1da39c5fd9a6e007a532553a1ff5b40d
A359964
Refactorable numbers (A033950) having more divisors than all smaller refactorable numbers.
[ "1", "2", "8", "12", "24", "36", "60", "180", "240", "360", "720", "1260", "1680", "3360", "5040", "10080", "15120", "20160", "25200", "30240", "55440", "100800", "110880", "221760", "277200", "443520", "665280", "720720", "1108800", "1441440", "2494800", "2882880", "3603600", "5765760", "8648640", "12972960", "14414400", "25945920", "28828800" ]
[ "nonn" ]
12
0
5
[ "A000005", "A002182", "A033950", "A073904", "A110821", "A335317", "A356078", "A359963", "A359964" ]
null
Amiram Eldar, Jan 20 2023
2023-01-23T02:33:10
oeisdata/seq/A359/A359964.seq
30b6193f761b89c51aef8ced395edd48
A359965
a(n) is the least arithmetic number (A003601) having exactly n divisors.
[ "1", "3", "49", "6", "14641", "20", "594823321", "30", "8281", "304", "41426511213649", "60", "491258904256726154641", "832", "717409", "168", "160470643909878751793805444097921", "612", "114445997944945591651333831028437092270721", "432", "87616", "44032", "6111571184724799803076702357055363809", "420", "13521270961" ]
[ "nonn" ]
10
0
5
[ "A000005", "A000203", "A003601", "A005179", "A073904", "A359963", "A359965" ]
null
Amiram Eldar, Jan 20 2023
2023-01-21T03:44:26
oeisdata/seq/A359/A359965.seq
2c9dfc25ad1cb469a84e8c1d4ee3f866
A359966
Expansion of Product_{k>=2} (1 - x^(k^2-1)) in powers of x.
[ "1", "0", "0", "-1", "0", "0", "0", "0", "-1", "0", "0", "1", "0", "0", "0", "-1", "0", "0", "1", "0", "0", "0", "0", "1", "-1", "0", "-1", "1", "0", "0", "0", "0", "1", "0", "0", "-2", "0", "0", "1", "1", "0", "0", "-1", "1", "0", "0", "-1", "-1", "-1", "0", "2", "1", "0", "-1", "0", "0", "1", "0", "-1", "0", "0", "1", "-1", "0", "0", "0", "0", "-1", "0", "0", "1", "0", "1", "0", "-1", "-1", "0", "1", "1", "0", "-2", "-1", "1", "3" ]
[ "sign" ]
12
0
5
[ "A005563", "A276516", "A359936", "A359966", "A359967" ]
null
Seiichi Manyama, Jan 20 2023
2023-01-21T02:02:03
oeisdata/seq/A359/A359966.seq
18ec6b47a90791eb9247ed28f45a0451
A359967
a(n) = Sum_{d|n, d+1 is square} d.
[ "0", "0", "3", "0", "0", "3", "0", "8", "3", "0", "0", "3", "0", "0", "18", "8", "0", "3", "0", "0", "3", "0", "0", "35", "0", "0", "3", "0", "0", "18", "0", "8", "3", "0", "35", "3", "0", "0", "3", "8", "0", "3", "0", "0", "18", "0", "0", "83", "0", "0", "3", "0", "0", "3", "0", "8", "3", "0", "0", "18", "0", "0", "66", "8", "0", "3", "0", "0", "3", "35", "0", "35", "0", "0", "18", "0", "0", "3", "0", "88", "3", "0", "0", "3", "0", "0" ]
[ "nonn" ]
19
0
5
[ "A005563", "A035316", "A179952", "A359937", "A359967" ]
null
Seiichi Manyama, Jan 20 2023
2023-01-21T03:52:17
oeisdata/seq/A359/A359967.seq
43d3ec301d0f78b875a46b8fb494cb14
A359968
Number of vertices formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions equal the Farey series of order n.
[ "3", "6", "37", "195", "1467", "3408", "17113", "40435", "109638", "191718", "572939", "842487", "2139708", "3231583", "5261013" ]
[ "nonn", "more" ]
14
0
5
[ "A005728", "A358887", "A358949", "A359690", "A359968", "A359969", "A359970", "A359971", "A359974", "A360042" ]
null
Scott R. Shannon and N. J. A. Sloane, Jan 20 2023
2023-01-30T10:32:29
oeisdata/seq/A359/A359968.seq
e87982c9e8412f199c195ab376ff4595
A359969
Number of regions formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions equal the Farey series of order n.
[ "1", "5", "48", "239", "1798", "3950", "19953", "46007", "123338", "213793", "637960", "930635", "2361080", "3542822", "5736344" ]
[ "nonn", "more" ]
11
0
5
[ "A005728", "A358886", "A358948", "A359690", "A359968", "A359969", "A359970", "A359971", "A359975", "A360042" ]
null
Scott R. Shannon and N. J. A. Sloane, Jan 20 2023
2023-01-30T10:32:40
oeisdata/seq/A359/A359969.seq
a76186c650d112683b17acd6fe761e6b
A359970
Number of edges formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions equal the Farey series of order n.
[ "3", "10", "84", "433", "3264", "7357", "37065", "86441", "232975", "405510", "1210898", "1773121", "4500787", "6774404", "10997356" ]
[ "nonn", "more" ]
10
0
5
[ "A005728", "A358888", "A358950", "A359693", "A359968", "A359969", "A359970", "A359971", "A359976", "A360042" ]
null
Scott R. Shannon and N. J. A. Sloane, Jan 20 2023
2023-01-30T10:32:49
oeisdata/seq/A359/A359970.seq
5483396be49523a8955641207202f929
A359971
Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions equal the Farey series of order n.
[ "1", "5", "33", "15", "108", "126", "5", "727", "1031", "38", "2", "1314", "2452", "167", "15", "2", "6811", "12102", "988", "52", "14904", "27626", "3255", "214", "4", "2", "2", "39172", "73289", "10062", "795", "19", "1", "65833", "127951", "18476", "1464", "64", "5", "201643", "370880", "59630", "5548", "250", "7", "2", "288196", "541258", "91037", "9692", "428", "20", "4", "741597", "1351301", "239180", "27510", "1434", "58" ]
[ "nonn", "tabf" ]
23
0
5
[ "A005728", "A358889", "A358951", "A359694", "A359968", "A359969", "A359970", "A359971", "A359977", "A360042" ]
null
Scott R. Shannon and N. J. A. Sloane, Jan 20 2023
2023-01-30T10:32:59
oeisdata/seq/A359/A359971.seq
93ddf1c6b7d3dafb8ccb33a69686796a
A359972
Number of 4-shaft weaving patterns, threaded 1,2,3,4, with n rows, up to symmetries.
[ "0", "3", "30", "465", "5591", "71722", "893120", "11228834", "141465194" ]
[ "nonn", "more" ]
70
0
5
null
null
Jeffrey Shallit, Jan 22 2023
2023-02-05T11:52:46
oeisdata/seq/A359/A359972.seq
7218867e3a9eaf39cbcc45b3dec8e1b9
A359973
Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the concatenation of the decimal digits of n and a(n) or of a(n) and n yields a prime number.
[ "1", "3", "2", "7", "9", "13", "4", "11", "5", "19", "8", "17", "6", "23", "31", "21", "12", "47", "10", "27", "16", "37", "14", "41", "39", "33", "20", "43", "32", "49", "15", "29", "26", "57", "59", "71", "22", "51", "25", "73", "24", "53", "28", "63", "61", "79", "18", "77", "30", "81", "38", "97", "42", "83", "69", "89", "34", "67", "35", "91", "45", "87", "44", "109", "99", "103", "58" ]
[ "nonn", "base" ]
15
0
5
[ "A083569", "A088629", "A359973" ]
null
Rémy Sigrist, Jan 20 2023
2023-01-22T08:37:38
oeisdata/seq/A359/A359973.seq
4c451091a447bc2a6c69ea0a07d5577c
A359974
Number of vertices formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions on one edge equal the Farey series of order n while on the other they divide its length into n equal segments.
[ "3", "6", "26", "93", "424", "876", "2785", "5542", "11575", "18761", "40249", "57399", "109376", "155965", "227884", "322377", "532454", "676282", "1056010", "1334975", "1767798", "2240664", "3252047", "3882192", "5226897" ]
[ "nonn", "more" ]
13
0
5
[ "A005728", "A358887", "A358949", "A359690", "A359968", "A359974", "A359975", "A359976", "A359977" ]
null
Scott R. Shannon and N. J. A. Sloane, Jan 20 2023
2023-01-30T10:33:36
oeisdata/seq/A359/A359974.seq
17409e7afbf69567e880346da7589aa5
A359975
Number of regions formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions on one edge equal the Farey series of order n while on the other they divide its length into n equal segments.
[ "1", "5", "30", "110", "479", "993", "3102", "6135", "12748", "20680", "43907", "62753", "118746", "168892", "246513", "348176", "571980", "725956", "1129035", "1426393", "1887096", "2387945", "3454566", "4123548", "5543837" ]
[ "nonn", "more" ]
14
0
5
[ "A005728", "A358886", "A358948", "A359690", "A359969", "A359974", "A359975", "A359976", "A359977" ]
null
Scott R. Shannon and N. J. A. Sloane, Jan 20 2023
2023-01-30T10:33:44
oeisdata/seq/A359/A359975.seq
2536baed1a2d34043547ba4d4b24da6c
A359976
Number of edges formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions on one edge equal the Farey series of order n while on the other they divide its length into n equal segments.
[ "3", "10", "55", "202", "902", "1868", "5886", "11676", "24322", "39440", "84155", "120151", "228121", "324856", "474396", "670552", "1104433", "1402237", "2185044", "2761367", "3654893", "4628608", "6706612", "8005739", "10770733" ]
[ "nonn", "more" ]
14
0
5
[ "A005728", "A358888", "A358950", "A359693", "A359970", "A359974", "A359975", "A359976", "A359977" ]
null
Scott R. Shannon and N. J. A. Sloane, Jan 20 2023
2023-01-30T10:33:52
oeisdata/seq/A359/A359976.seq
bc80df22e4c968e0c70c8a21fd26c2d8
A359977
Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions on one edge equal the Farey series of order n while on the other they divide its length into n equal segments.
[ "1", "5", "20", "8", "2", "50", "57", "3", "169", "274", "31", "5", "303", "646", "41", "2", "1", "889", "2011", "179", "21", "2", "1685", "4025", "388", "33", "4", "3466", "8283", "925", "67", "7", "5624", "13442", "1498", "106", "9", "1", "11896", "27907", "3718", "354", "30", "2", "16976", "40100", "5182", "461", "33", "1", "32506", "73806", "11249", "1118", "61", "6", "46187", "104453", "16380", "1747", "123", "1", "1" ]
[ "nonn", "tabf" ]
14
0
5
[ "A005728", "A358889", "A358951", "A359694", "A359971", "A359974", "A359975", "A359976", "A359977" ]
null
Scott R. Shannon and N. J. A. Sloane, Jan 20 2023
2023-01-30T10:34:01
oeisdata/seq/A359/A359977.seq
5bb2ece80b20755a1b879a8156e8f37b
A359978
Prime numbers whose decimal representation can be split into two nonempty parts without leading 0, say x and y (in that order), and such that the concatenation of y and x yields a different prime number.
[ "13", "17", "31", "37", "71", "73", "79", "97", "113", "127", "131", "149", "157", "163", "173", "181", "191", "197", "199", "271", "277", "311", "313", "317", "331", "337", "359", "367", "373", "379", "397", "419", "479", "491", "571", "577", "593", "617", "631", "673", "719", "727", "733", "739", "757", "761", "787", "797", "811", "839", "877", "911", "919", "937" ]
[ "nonn", "base" ]
9
0
5
[ "A061461", "A225035", "A246944", "A359978" ]
null
Rémy Sigrist, Jan 20 2023
2023-01-22T16:02:57
oeisdata/seq/A359/A359978.seq
7df2021f442e44cff9c4d2ba1e68bac6
A359979
Irregular table T(n,k), n >= 0 and k >= 0, read by rows with T(n + 3*k,k) = A008619(n).
[ "1", "1", "2", "2", "1", "3", "1", "3", "2", "4", "2", "1", "4", "3", "1", "5", "3", "2", "5", "4", "2", "1", "6", "4", "3", "1", "6", "4", "3", "2", "7", "5", "4", "2", "1", "7", "6", "4", "3", "1", "8", "6", "5", "3", "2", "8", "7", "5", "4", "2", "1", "9", "7", "6", "4", "3", "1", "9", "8", "6", "5", "3", "2", "10", "8", "7", "5", "4", "2", "1", "10", "9", "7", "6", "4", "3", "1", "11", "9", "8", "6", "5", "3", "2" ]
[ "nonn", "tabf" ]
8
0
5
[ "A001399", "A008619", "A008620", "A008642", "A008805", "A359979" ]
null
Philippe Deléham, Jan 20 2023
2023-02-04T11:09:28
oeisdata/seq/A359/A359979.seq
a7a0c7ad1fac7e2f90a7238caf13c56a
A359980
Expansion of Product_{k>=0} (1 - x^(k^2+2)) in powers of x.
[ "1", "0", "-1", "-1", "0", "1", "-1", "0", "1", "1", "0", "-2", "0", "1", "1", "0", "-1", "1", "-1", "-1", "0", "1", "1", "-1", "1", "0", "-1", "-2", "0", "3", "1", "-1", "-2", "1", "1", "-2", "-1", "1", "2", "0", "-1", "0", "0", "0", "0", "1", "0", "-1", "-1", "1", "1", "-3", "-1", "2", "3", "-1", "-2", "2", "1", "-1", "-2", "0", "2", "0", "-1", "0", "-1", "-1", "-1", "3", "3", "-2", "-1", "1", "1", "-3", "-3", "3", "4", "0" ]
[ "sign", "look" ]
19
0
5
[ "A276516", "A359936", "A359966", "A359980", "A360001", "A360002", "A360003" ]
null
Seiichi Manyama, Jan 21 2023
2023-01-21T11:51:46
oeisdata/seq/A359/A359980.seq
87138779ff92e6d60a9c1ac7d1ff0303
A359981
Nonsquares which can be expressed as the product of a number and its digit reversal.
[ "10", "40", "90", "160", "250", "252", "360", "403", "490", "574", "640", "736", "765", "810", "976", "1000", "1008", "1207", "1210", "1300", "1458", "1462", "1612", "1729", "1855", "1944", "2268", "2296", "2430", "2520", "2668", "2701", "2944", "3154", "3478", "3627", "3640", "4000", "4030", "4032", "4275", "4606", "4840", "4930", "5092", "5605", "5740" ]
[ "nonn", "base" ]
13
0
5
[ "A000005", "A000037", "A000290", "A004086", "A027750", "A305231", "A325148", "A359981" ]
null
Stefano Spezia, Jan 20 2023
2023-01-28T12:02:11
oeisdata/seq/A359/A359981.seq
1443e327c463fd99c9cfe62ca710b63a
A359982
Numbers whose digits are distinct nonprimes and are not a permutation of a smaller such number.
[ "0", "1", "4", "6", "8", "9", "10", "14", "16", "18", "19", "40", "46", "48", "49", "60", "68", "69", "80", "89", "90", "104", "106", "108", "109", "146", "148", "149", "168", "169", "189", "406", "408", "409", "468", "469", "489", "608", "609", "689", "809", "1046", "1048", "1049", "1068", "1069", "1089", "1468", "1469", "1489", "1689", "4068", "4069", "4089", "4689", "6089", "10468", "10469", "10489", "10689", "14689", "40689", "104689" ]
[ "nonn", "base", "fini", "full" ]
30
0
5
[ "A062115", "A124673", "A359982" ]
null
Glen Gilchrist, Jan 20 2023
2023-05-03T15:02:53
oeisdata/seq/A359/A359982.seq
559208392ef6e513e089399a0c4d5589
A359983
Numbers with exactly two nonzero decimal digits and not ending with 0.
[ "11", "12", "13", "14", "15", "16", "17", "18", "19", "21", "22", "23", "24", "25", "26", "27", "28", "29", "31", "32", "33", "34", "35", "36", "37", "38", "39", "41", "42", "43", "44", "45", "46", "47", "48", "49", "51", "52", "53", "54", "55", "56", "57", "58", "59", "61", "62", "63", "64", "65", "66", "67", "68", "69", "71", "72", "73", "74", "75", "76", "77", "78", "79", "81", "82", "83", "84", "85", "86", "87", "88", "89", "91", "92", "93", "94", "95", "96", "97", "98", "99", "101", "102", "103", "104", "105", "106", "107", "108", "109", "201" ]
[ "nonn", "base", "easy" ]
7
0
5
[ "A038687", "A359098", "A359651", "A359983" ]
null
Charles R Greathouse IV, Jan 20 2023
2023-01-24T10:28:39
oeisdata/seq/A359/A359983.seq
9b6f26f702b0c81b6e9f44b74ef14f39
A359984
Number of non-crossing antichain covers of {1,...,n} without singletons.
[ "1", "0", "1", "5", "40", "372", "3815", "41652", "474980", "5591912", "67454545", "829438722", "10358083621", "131013535954", "1674940506728", "21608978465341", "280976960703472", "3678460005228692", "48446069275681169", "641429612434785006", "8532711384899213885", "113988520118626013998" ]
[ "nonn" ]
12
0
5
[ "A054726", "A324167", "A324168", "A324169", "A359984" ]
null
Andrew Howroyd, Jan 20 2023
2023-03-11T15:07:51
oeisdata/seq/A359/A359984.seq
40a6899e8ec36f9d70ac5a483fabf71a
A359985
Triangle read by rows: T(n,k) is the number of quasi series-parallel matroids on [n] with rank k, 0 <= k <= n.
[ "1", "1", "1", "1", "3", "1", "1", "7", "7", "1", "1", "15", "35", "15", "1", "1", "31", "155", "155", "31", "1", "1", "63", "651", "1365", "651", "63", "1", "1", "127", "2667", "10941", "10941", "2667", "127", "1", "1", "255", "10795", "82215", "156597", "82215", "10795", "255", "1", "1", "511", "43435", "589135", "1988007", "1988007", "589135", "43435", "511", "1" ]
[ "nonn", "tabl" ]
13
0
5
[ "A000012", "A000225", "A006095", "A022166", "A140945", "A359985", "A359986" ]
null
Andrew Howroyd, Mar 08 2023
2024-10-15T15:08:24
oeisdata/seq/A359/A359985.seq
c37793ea7eaf6760e96bd51042f93718
A359986
Number of quasi series-parallel matroids on [n].
[ "1", "2", "5", "16", "67", "374", "2795", "27472", "343129", "5242178", "94775045", "1976279584", "46619596363", "1225918376726", "35526110971595", "1124201803439968", "38555828073355441", "1424165085382532162", "56356111920073052165", "2378150844047351691376", "106590791633357076443347" ]
[ "nonn" ]
8
0
5
[ "A359985", "A359986" ]
null
Andrew Howroyd, Mar 08 2023
2024-10-15T15:07:19
oeisdata/seq/A359/A359986.seq
7a3cc18983aceefa595d45921815012c
A359987
Number of edge cuts in the n-ladder graph P_2 X P_n.
[ "1", "11", "105", "919", "7713", "63351", "514321", "4148839", "33347041", "267489431", "2143168305", "17160184519", "137349160833", "1099102033911", "8794224638161", "70360221445159", "562911076526881", "4503422288363351", "36027988077717105", "288226686123491719", "2305826176955087553", "18446667292472959671" ]
[ "nonn", "easy" ]
16
0
5
[ "A013730", "A107839", "A356828", "A359621", "A359622", "A359987", "A359989", "A359990" ]
null
Andrew Howroyd, Jan 28 2023
2024-11-03T12:24:34
oeisdata/seq/A359/A359987.seq
c99b55c72a7bc7983b894ac4ba5b8419
A359988
Number of edge cuts in the 3 X n grid graph.
[ "3", "105", "3665", "123215", "4051679", "131630449", "4248037953", "136587740399", "4382607093471", "140457446235441", "4498520188148993", "144023056568886959", "4610014925578108703", "147543642097619999089", "4721816707356538941633", "151105755554498621737583", "4835522406931884652356447" ]
[ "nonn", "easy" ]
8
0
5
[ "A013823", "A158453", "A359987", "A359988", "A359990" ]
null
Andrew Howroyd, Jan 28 2023
2023-01-28T22:07:32
oeisdata/seq/A359/A359988.seq
64b402771189ecb2391ce1c52036c857
A359989
Number of edge cuts in the n X n grid graph.
[ "0", "11", "3665", "16222021", "1089224690733", "1150229180575982641", "19332960184149905415396841", "5191795779341747010730275139276101", "22300392508126626453613075681944644703634073", "1532492114568208344599582951444206568577948454351297761" ]
[ "nonn" ]
7
0
5
[ "A053765", "A286913", "A359989", "A359990", "A359992" ]
null
Andrew Howroyd, Jan 28 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359989.seq
e6344aeacf53e3bfb24dc885d4900fde
A359990
Array read by antidiagonals: T(m,n) is the number of edge cuts in the grid graph P_m X P_n.
[ "0", "1", "1", "3", "11", "3", "7", "105", "105", "7", "15", "919", "3665", "919", "15", "31", "7713", "123215", "123215", "7713", "31", "63", "63351", "4051679", "16222021", "4051679", "63351", "63", "127", "514321", "131630449", "2108725953", "2108725953", "131630449", "514321", "127", "255", "4148839", "4248037953", "272179739279", "1089224690733", "272179739279", "4248037953", "4148839", "255" ]
[ "nonn", "tabl" ]
8
0
5
[ "A000225", "A141387", "A359987", "A359988", "A359989", "A359990", "A359993" ]
null
Andrew Howroyd, Jan 28 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359990.seq
0e124dc4d17f20660567ab995cfedbdd
A359991
Number of connected spanning subgraphs in the 4 X n grid graph.
[ "1", "105", "7857", "555195", "38757695", "2698167665", "187715481077", "13057666054455", "908271228919067", "63177423571626685", "4394479113198329137", "305669914361091938915", "21261697652022553831895", "1478914849135091196256585", "102869919107895518546358701" ]
[ "nonn", "easy" ]
8
0
5
[ "A359991", "A359993" ]
null
Andrew Howroyd, Jan 28 2023
2023-01-28T22:07:28
oeisdata/seq/A359/A359991.seq
8642b7bbda24d02de9354a12dee836d3
A359992
Number of connected spanning subgraphs in the n X n grid graph.
[ "1", "5", "431", "555195", "10286937043", "2692324030864335", "9852929684161379901975", "501079193080617800221189943995", "352690403996687922642590703716802346343", "3426297680513758764075706102615040790667832304415", "458508006189588425325361635000918336126387961057365005349963" ]
[ "nonn" ]
13
0
5
[ "A007341", "A053765", "A080691", "A286913", "A359989", "A359992", "A359993" ]
null
Andrew Howroyd, Jan 28 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359992.seq
3db01adafeb935b4e8650f760ea42884
A359993
Array read by antidiagonals: T(m,n) is the number of connected spanning subgraphs in the grid graph P_m X P_n.
[ "1", "1", "1", "1", "5", "1", "1", "23", "23", "1", "1", "105", "431", "105", "1", "1", "479", "7857", "7857", "479", "1", "1", "2185", "142625", "555195", "142625", "2185", "1", "1", "9967", "2587279", "38757695", "38757695", "2587279", "9967", "1", "1", "45465", "46929343", "2698167665", "10286937043", "2698167665", "46929343", "45465", "1" ]
[ "nonn", "tabl" ]
13
0
5
[ "A000012", "A107839", "A116469", "A158453", "A286912", "A287151", "A359990", "A359991", "A359992", "A359993", "A360194" ]
null
Andrew Howroyd, Jan 28 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359993.seq
5a3ee006daf4d965fd5d0d6e0c693989
A359994
Independence number of the 2-Fibonacci digraph of order n.
[ "1", "1", "2", "3", "6", "9", "16", "25", "44", "67", "115" ]
[ "nonn", "more" ]
9
0
5
[ "A006946", "A359994", "A359995", "A359996", "A360000" ]
null
Pontus von Brömssen, Jan 21 2023
2023-11-12T09:32:03
oeisdata/seq/A359/A359994.seq
5945fd571cd4a6ac8f2e9727c1b32001
A359995
Number of maximal independent sets in the 2-Fibonacci digraph of order n.
[ "2", "3", "4", "10", "32", "184", "5110", "681454" ]
[ "nonn", "more" ]
5
0
5
[ "A333077", "A359994", "A359995", "A359996", "A360000" ]
null
Pontus von Brömssen, Jan 21 2023
2023-01-22T08:40:20
oeisdata/seq/A359/A359995.seq
d6fb9bfb9ecc5b84842920c284833acc
A359996
Number of maximum independent sets in the 2-Fibonacci digraph of order n.
[ "2", "3", "4", "10", "3", "42", "12", "706" ]
[ "nonn", "more" ]
6
0
5
[ "A333078", "A359994", "A359995", "A359996", "A360000" ]
null
Pontus von Brömssen, Jan 21 2023
2023-01-22T08:40:27
oeisdata/seq/A359/A359996.seq
945cfb048d5423532bc497d8058235d8
A359997
Irregular triangle read by rows: T(n,k) is the number of directed cycles of length k in the 2-Fibonacci digraph of order n.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "2", "2", "2", "1", "1", "1", "1", "2", "2", "4", "3", "5", "4", "7", "6", "6", "6", "4", "4", "2", "2", "1", "1", "1", "1", "2", "2", "4", "5", "5", "6", "8", "10", "15", "20", "20", "24", "23", "19", "18", "20", "30", "30", "36", "36", "16", "0", "28", "28", "28" ]
[ "nonn", "tabf" ]
19
0
5
[ "A006206", "A080023", "A344018", "A359997", "A359998", "A359999", "A360000" ]
null
Pontus von Brömssen, Jan 21 2023
2023-05-30T19:43:53
oeisdata/seq/A359/A359997.seq
eaabab108a8567d36e9d6ae5a86b499a
A359998
Number of longest directed cycles in the 2-Fibonacci digraph of order n.
[ "1", "1", "1", "1", "2", "2", "28", "216", "65200", "167084480" ]
[ "nonn", "more" ]
9
0
5
[ "A016031", "A080023", "A359997", "A359998", "A360000" ]
null
Pontus von Brömssen, Jan 21 2023
2023-01-24T17:42:51
oeisdata/seq/A359/A359998.seq
2a81006904d4ae450ea87669bb246c37
A359999
Most common cycle length in the 2-Fibonacci digraph of order n. In case of ties, choose the largest length.
[ "2", "3", "4", "5", "11", "11", "24", "32", "59", "92" ]
[ "nonn", "more" ]
9
0
5
[ "A359997", "A359999", "A360000" ]
null
Pontus von Brömssen, Jan 21 2023
2023-01-24T17:42:36
oeisdata/seq/A359/A359999.seq
d732a760eb4a143d0c3df48367324acf
A360000
Number of directed cycles in the 2-Fibonacci digraph of order n.
[ "2", "3", "4", "8", "16", "61", "437", "17766", "5885824", "111327315589" ]
[ "nonn", "more" ]
12
0
5
[ "A000045", "A306522", "A359997", "A359998", "A359999", "A360000" ]
null
Pontus von Brömssen, Jan 21 2023
2023-01-25T02:12:47
oeisdata/seq/A360/A360000.seq
01f63daf610af04cc04a9161f77f874a