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1999-12-11 03:00:00
2025-04-28 00:58:08
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A357401
Coefficients in the power series expansion of 1/Sum_{n=-oo..+oo} n * x^(2*n+1) * (1 - x^n)^(n+1).
[ "1", "0", "1", "0", "-2", "8", "-14", "16", "-7", "-24", "103", "-232", "334", "-256", "-211", "1400", "-3562", "6048", "-6470", "512", "17788", "-53720", "102983", "-134832", "76147", "187960", "-776169", "1690880", "-2558499", "2270952", "1214672", "-10443024", "26674201", "-45822896", "51953043", "-11147384", "-126256811", "401311496" ]
[ "sign" ]
16
1
5
[ "A357400", "A357401", "A357406" ]
null
Paul D. Hanna, Sep 26 2022
2022-09-29T17:46:40
oeisdata/seq/A357/A357401.seq
ee2d22226574195044b1ae90f6f24f6a
A357402
Coefficients in the power series A(x) such that: 2 = Sum_{n=-oo..+oo} x^(2*n+1) * (1 - x^n)^(n+1) * A(x)^n.
[ "1", "2", "8", "42", "236", "1420", "8976", "58644", "393200", "2689522", "18694164", "131658910", "937490780", "6737990172", "48816739048", "356142597586", "2614103310384", "19291118713324", "143044431901580", "1065237986700788", "7963426677825000", "59741019702076168", "449601401992383464", "3393484429948103486" ]
[ "nonn" ]
8
0
2
[ "A356783", "A357400", "A357402", "A357403", "A357404", "A357405" ]
null
Paul D. Hanna, Sep 26 2022
2022-10-08T00:26:48
oeisdata/seq/A357/A357402.seq
aa90b9bacc3f643a4301cfecc65d5b18
A357403
Coefficients in the power series A(x) such that: 3 = Sum_{n=-oo..+oo} x^(2*n+1) * (1 - x^n)^(n+1) * A(x)^n.
[ "1", "3", "18", "138", "1161", "10470", "98979", "967719", "9705378", "99290130", "1032123366", "10870453785", "115749660723", "1244016993747", "13477172250201", "147021521096445", "1613619363015645", "17805435511256394", "197414608524234453", "2198189145649419426", "24571174933256703567", "275615684936993421462" ]
[ "nonn" ]
6
0
2
[ "A356783", "A357400", "A357402", "A357403", "A357404", "A357405" ]
null
Paul D. Hanna, Sep 26 2022
2022-09-27T12:00:18
oeisdata/seq/A357/A357403.seq
00189eaae64f6ed446ea3a030f8a4fcb
A357404
Coefficients in the power series A(x) such that: 4 = Sum_{n=-oo..+oo} x^(2*n+1) * (1 - x^n)^(n+1) * A(x)^n.
[ "1", "4", "32", "324", "3632", "43640", "549472", "7154952", "95563392", "1301943972", "18022506736", "252768034908", "3584103003152", "51294399688504", "739984677348512", "10749373940462452", "157101410692820448", "2308378616597302488", "34080671255517914992", "505321131709023383016", "7521442675843527317728" ]
[ "nonn" ]
6
0
2
[ "A356783", "A357400", "A357402", "A357403", "A357404", "A357405" ]
null
Paul D. Hanna, Sep 26 2022
2022-09-27T12:24:27
oeisdata/seq/A357/A357404.seq
16bd24eda3f7b25f717212205862abe6
A357405
Coefficients in the power series A(x) such that: 5 = Sum_{n=-oo..+oo} x^(2*n+1) * (1 - x^n)^(n+1) * A(x)^n.
[ "1", "5", "50", "630", "8825", "132490", "2084115", "33903705", "565697930", "9627904690", "166493454330", "2917050253615", "51670197054515", "923774673549045", "16647699155752645", "302098954307654995", "5515438344643031325", "101237254225602624790", "1867129260849076888865", "34583287418814030368150" ]
[ "nonn" ]
6
0
2
[ "A356783", "A357400", "A357402", "A357403", "A357404", "A357405" ]
null
Paul D. Hanna, Sep 26 2022
2022-09-27T12:49:10
oeisdata/seq/A357/A357405.seq
424af4fe5f362e38ec8d79800bcc21b7
A357406
Coefficients in the power series expansion of A(x) = Sum_{n=-oo..+oo} n * x^(2*n+2) * (1 - x^n)^(n+1).
[ "1", "0", "-1", "0", "3", "-8", "9", "0", "-10", "0", "24", "-24", "0", "0", "15", "0", "9", "-80", "90", "0", "-43", "0", "57", "-80", "13", "0", "175", "-200", "15", "-120", "313", "0", "-346", "0", "450", "-168", "19", "-744", "830", "0", "21", "-224", "-287", "0", "405", "0", "1014", "-1968", "25", "0", "2813", "-784", "-2448", "-360", "1575", "0", "2765", "-3520", "450", "-440", "31" ]
[ "sign" ]
9
0
5
[ "A356774", "A357401", "A357406" ]
null
Paul D. Hanna, Sep 27 2022
2022-10-08T15:16:30
oeisdata/seq/A357/A357406.seq
eb0aa8549408442d1473f2a2af01682b
A357407
a(n) = coefficient of x^n, n >= 0, in A(x) = exp( Sum_{n>=1} A183204(n)*x^n/n ), where A183204 equals the central terms of triangle A181544.
[ "1", "4", "32", "360", "4964", "78064", "1344020", "24708928", "477282794", "9580852360", "198322047840", "4209371498256", "91221481924426", "2011834246746792", "45039165331725264", "1021419638492387856", "23426910170090512779", "542666070296546760492", "12681393784980089971368" ]
[ "nonn" ]
10
0
2
[ "A181544", "A183204", "A357407" ]
null
Paul D. Hanna, Oct 19 2022
2023-03-14T05:22:01
oeisdata/seq/A357/A357407.seq
4957922f4c35675e7478e5d70a70735d
A357408
a(n) is the least sum n + y such that 1/n + 1/y = 1/z with gcd(n,y,z) = 1, for some integers y and z.
[ "4", "9", "16", "25", "9", "49", "64", "81", "25", "121", "16", "169", "49", "25", "256", "289", "81", "361", "25", "49", "121", "529", "64", "625", "169", "729", "49", "841", "36", "961", "1024", "121", "289", "49", "81", "1369", "361", "169", "64", "1681", "49", "1849", "121", "81", "529", "2209", "256", "2401", "625", "289", "169", "2809", "729", "121", "64", "361" ]
[ "nonn" ]
23
2
1
[ "A000290", "A034699", "A357408" ]
null
Michel Lagneau, Sep 26 2022
2022-11-06T08:38:25
oeisdata/seq/A357/A357408.seq
9632fa96dae87a342d9f726b71044872
A357409
a(n) is the maximum number of positive numbers in a set of n consecutive positive or negative odd numbers such that the number of pairs that add to a power of 2 is maximal.
[ "1", "2", "3", "3", "4", "5", "5", "6", "6", "7", "7", "8", "9", "9", "10", "10", "11", "11", "12", "12", "13", "13", "14", "14", "15", "15", "17", "18", "18", "19", "19", "20", "20", "21", "21", "22", "22", "23", "23", "24", "24", "25", "25", "26", "26", "27", "27", "28", "28", "29", "29", "30", "30", "31", "31", "32", "33", "33", "34", "34", "35", "35", "36", "36", "37", "37", "38", "38", "39" ]
[ "nonn" ]
39
1
2
[ "A274089", "A347301", "A352178", "A357409", "A357574" ]
null
Thomas Scheuerle, Sep 26 2022
2022-10-27T05:33:49
oeisdata/seq/A357/A357409.seq
2747c8563d590a7469f072aefd9b1baa
A357410
a(n) is the number of covering relations in the poset P of n X n idempotent matrices over GF(2) ordered by A <= B if and only if AB = BA = A.
[ "0", "1", "12", "224", "6960", "397792", "42001344", "8547291008", "3336917303040", "2565880599084544", "3852698988517260288", "11517943538435677485056", "67829192662051610706309120", "799669932659456441970547744768", "18652191511341505602408972738871296", "873360272626100960024734923878091948032" ]
[ "nonn" ]
18
0
3
[ "A002884", "A132186", "A296548", "A342245", "A357410" ]
null
Geoffrey Critzer, Sep 26 2022
2022-09-26T20:03:40
oeisdata/seq/A357/A357410.seq
6cceb1351546e24a2d36a2e2ffe7a4d0
A357411
Number of nonempty subsets of {1..n} whose elements have an odd harmonic mean.
[ "1", "1", "2", "2", "3", "5", "6", "6", "7", "9", "10", "10", "11", "13", "26", "26", "27", "45", "46", "74", "93", "99", "100", "162", "163", "165", "166", "458", "459", "865", "866", "866", "1647", "1669", "2724" ]
[ "nonn", "more" ]
25
1
3
[ "A339453", "A357355", "A357411", "A357412", "A357413", "A357415" ]
null
Ilya Gutkovskiy, Sep 27 2022
2022-09-30T14:37:07
oeisdata/seq/A357/A357411.seq
e702f6176024a899e4650dcaa2cee656
A357412
Number of nonempty subsets of {1..n} whose elements have an even harmonic mean.
[ "0", "1", "1", "2", "2", "7", "7", "8", "8", "9", "9", "16", "16", "17", "27", "28", "28", "55", "55", "106", "110", "111", "111", "216", "216", "217", "217", "634", "634", "1155", "1155", "1156", "2286", "2287", "3749" ]
[ "nonn", "more" ]
25
1
4
[ "A339453", "A357356", "A357411", "A357412", "A357414", "A357416" ]
null
Ilya Gutkovskiy, Sep 27 2022
2022-09-30T14:36:17
oeisdata/seq/A357/A357412.seq
cf523a23c1870622429c8de30d639619
A357413
Number of nonempty subsets of {1..n} whose elements have an odd geometric mean.
[ "0", "1", "1", "2", "2", "3", "3", "4", "4", "7", "7", "8", "8", "9", "9", "10", "10", "11", "11", "12", "12", "13", "13", "14", "14", "19", "19", "24", "24", "25", "25", "26", "26", "27", "27", "28", "28", "29", "29", "30", "30", "31", "31", "32", "32", "39", "39", "40", "40", "49", "49", "50", "50", "51", "51", "52", "52", "53", "53", "54", "54", "55", "55", "62", "62", "63", "63", "64", "64", "65", "65", "66", "66", "67", "67", "90", "90", "91", "91", "92", "92" ]
[ "nonn" ]
33
0
4
[ "A001055", "A326027", "A357355", "A357411", "A357413", "A357414", "A357415" ]
null
Ilya Gutkovskiy, Sep 27 2022
2025-03-07T07:49:41
oeisdata/seq/A357/A357413.seq
56a54a0b4cde9b62c3b2fe0e5dcc1736
A357414
Number of nonempty subsets of {1..n} whose elements have an even geometric mean.
[ "0", "0", "1", "1", "4", "4", "5", "5", "8", "12", "13", "13", "20", "20", "21", "21", "30", "30", "59", "59", "62", "62", "63", "63", "94", "104", "105", "187", "190", "190", "191", "191", "306", "306", "307", "307", "564", "564", "565", "565", "582", "582", "583", "583", "586", "600", "601", "601", "1120", "1134", "1275", "1275", "1278", "1278", "2125", "2125", "2144", "2144", "2145", "2145", "2360", "2360", "2361", "2381", "3938", "3938", "3939", "3939", "3942", "3942", "3943", "3943", "6560", "6560", "6561", "9663", "9666" ]
[ "nonn" ]
30
0
5
[ "A326027", "A357356", "A357412", "A357413", "A357414", "A357416" ]
null
Ilya Gutkovskiy, Sep 27 2022
2025-03-07T07:49:55
oeisdata/seq/A357/A357414.seq
c7541c98fb31b6eef94ffb5d7fcacc2e
A357415
Number of nonempty subsets of {1..n} whose elements have an odd root mean square.
[ "1", "1", "2", "2", "3", "3", "6", "6", "7", "9", "16", "26", "41", "85", "142", "254", "461", "825", "1454", "2506", "4535", "7987", "14352", "26178", "47861", "87945", "162486", "304864", "565217", "1064529", "1992628", "3742934", "7034489", "13214869", "24924676", "46926388", "88812537", "167903969", "318619708", "604909434", "1150800393" ]
[ "nonn" ]
16
1
3
[ "A339454", "A357355", "A357411", "A357413", "A357415", "A357416" ]
null
Ilya Gutkovskiy, Sep 27 2022
2025-03-25T13:29:55
oeisdata/seq/A357/A357415.seq
98b90b7c847471381276a752d83b89a3
A357416
Number of nonempty subsets of {1..n} whose elements have an even root mean square.
[ "0", "1", "1", "2", "2", "3", "3", "4", "8", "11", "13", "26", "46", "81", "169", "284", "482", "857", "1461", "2548", "4370", "7917", "14181", "25648", "47330", "87457", "163291", "302678", "568974", "1064393", "1993805", "3742588", "7030646", "13231519", "24871349", "46994382", "88657700", "167876827", "318263561", "604694212", "1150634498" ]
[ "nonn" ]
16
1
4
[ "A339454", "A357356", "A357412", "A357414", "A357415", "A357416" ]
null
Ilya Gutkovskiy, Sep 27 2022
2025-03-25T13:29:23
oeisdata/seq/A357/A357416.seq
729bfb393bcc105955ccdcffe5032bc1
A357417
Row sums of the triangular array A357431.
[ "1", "5", "12", "27", "43", "76", "109", "168", "218", "301", "383", "499", "591", "779", "904", "1153", "1322", "1555", "1817", "2143", "2379", "2790", "3164", "3627", "3957", "4546", "5034", "5599", "6062", "6937", "7456", "8369", "8973", "9896", "10678", "11663", "12430", "13732", "14618", "15920", "16996", "18471", "19570", "20934", "22189", "24080" ]
[ "nonn" ]
38
1
2
[ "A002411", "A357417", "A357431" ]
null
Tamas Sandor Nagy, Sep 27 2022
2022-11-20T05:54:38
oeisdata/seq/A357/A357417.seq
9434dae823877a67d90025d2954b8bc1
A357418
Decimal expansion of (207 - 33*sqrt(33))/32.
[ "5", "4", "4", "6", "6", "9", "7", "7", "0", "7", "5", "7", "6", "5", "7", "9", "4", "4", "5", "2", "9", "0", "5", "6", "9", "2", "3", "3", "9", "9", "2", "2", "9", "1", "4", "0", "5", "8", "5", "3", "5", "2", "2", "7", "7", "7", "0", "5", "2", "4", "5", "3", "7", "0", "8", "0", "9", "5", "0", "1", "3", "5", "8", "4", "7", "8", "9", "1", "4", "8", "8", "0", "9", "9", "7", "0", "5", "1", "4", "7", "8", "3", "7", "8", "2", "7", "6", "9", "6", "6", "7", "2", "8", "3", "1" ]
[ "nonn", "cons", "easy" ]
8
0
1
[ "A010488", "A357418" ]
null
Stefano Spezia, Sep 27 2022
2022-09-27T13:11:31
oeisdata/seq/A357/A357418.seq
828080f5e083957dd4be0704a7dd2e45
A357419
a(n) is the hafnian of the 2n X 2n symmetric Pascal matrix defined by M[i, j] = A007318(i + j - 2, i - 1).
[ "1", "1", "17", "4929", "23872137", "1901611778409", "2469317979267366913", "52019468048773355156225921", "17726418489020770628047341494927089", "97518325438289444681986165275143492027985129", "8648473129650550498122567373327602114148485950241817345" ]
[ "nonn", "hard" ]
16
0
3
[ "A006134", "A007318", "A095833", "A202038", "A320845", "A336114", "A336286", "A336400", "A338456", "A356481", "A356482", "A356483", "A356484", "A357419" ]
null
Stefano Spezia, Sep 27 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357419.seq
fec6eef8b62dcd000a29caab903d007c
A357420
a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = abs(i - j) if min(i, j) < max(i, j) <= 2*min(i, j), and otherwise 0.
[ "1", "1", "1", "8", "86", "878", "13730", "348760", "11622396", "509566864", "26894616012", "1701189027944", "125492778658096", "10738546182981256", "1049631636279244832", "117756049412699967072" ]
[ "nonn", "hard", "more" ]
14
0
4
[ "A000982", "A003983", "A007590", "A049581", "A051125", "A202038", "A336114", "A336286", "A336400", "A338456", "A352967", "A353452", "A353453", "A356481", "A356482", "A356483", "A356484", "A357279", "A357420" ]
null
Stefano Spezia, Sep 27 2022
2023-10-16T11:49:09
oeisdata/seq/A357/A357420.seq
974bcd360a8dcee6043381feb4d9a93f
A357421
a(n) is the hafnian of the 2n X 2n symmetric matrix whose generic element M[i,j] is equal to the digital root of i*j.
[ "1", "2", "54", "1377", "55350", "4164534", "217595322", "11974135554", "999599777190", "150051627647010", "11873389098337236" ]
[ "nonn", "base", "hard", "more" ]
11
0
2
[ "A003991", "A010888", "A202038", "A336114", "A336286", "A336400", "A338456", "A353109", "A353933", "A353974", "A356481", "A356482", "A356483", "A356484", "A357279", "A357421" ]
null
Stefano Spezia, Sep 27 2022
2023-10-15T09:26:39
oeisdata/seq/A357/A357421.seq
2f420336690c217182be1dd98a0a6124
A357422
E.g.f. satisfies A(x) * exp(A(x)) = -log(1 - x * exp(A(x))).
[ "0", "1", "1", "5", "34", "324", "3936", "58190", "1014056", "20354544", "462472800", "11733507312", "328809013776", "10086567702288", "336184985751720", "12097485061713480", "467445074411402496", "19303428522591336960", "848420150154305711616", "39543441411041750547648" ]
[ "nonn" ]
13
0
4
[ "A006963", "A141209", "A357343", "A357344", "A357345", "A357422" ]
null
Seiichi Manyama, Sep 27 2022
2024-09-09T09:34:10
oeisdata/seq/A357/A357422.seq
9ca22a6c52b810585465607de70ed40e
A357423
E.g.f. satisfies A(x) * exp(A(x)) = log(1 + x * exp(A(x))).
[ "0", "1", "-1", "-1", "10", "4", "-384", "818", "29800", "-205200", "-3612000", "56042832", "556589232", "-19091774352", "-70128589608", "8044430218680", "-25379500932864", "-4055729067351552", "48310659088501248", "2334746679051721536", "-58078273556262804480", "-1420062892415588203776" ]
[ "sign" ]
17
0
5
[ "A349587", "A357349", "A357350", "A357351", "A357423" ]
null
Seiichi Manyama, Sep 27 2022
2024-09-10T04:25:55
oeisdata/seq/A357/A357423.seq
bee0c3a40c10f587d3e2014de980e859
A357424
E.g.f. satisfies A(x) * exp(A(x)) = exp(x * exp(A(x))) - 1.
[ "0", "1", "1", "4", "21", "156", "1470", "16843", "227367", "3533974", "62163477", "1220852524", "26480355110", "628693388909", "16216901961481", "451609382251836", "13504072800481613", "431544662700594212", "14677503631085378170", "529370720888418692643", "20180856622352239827687" ]
[ "nonn" ]
16
0
4
[ "A052888", "A349588", "A357346", "A357347", "A357348", "A357424" ]
null
Seiichi Manyama, Sep 27 2022
2024-09-09T09:34:14
oeisdata/seq/A357/A357424.seq
6c1bf7bd3a473302fa280350822e82ff
A357425
Smallest number for which the sum of digits in fractional base 4/3 is n.
[ "0", "1", "2", "3", "5", "6", "7", "10", "11", "15", "21", "22", "23", "31", "39", "43", "54", "55", "74", "75", "101", "102", "103", "138", "139", "183", "187", "246", "247", "330", "331", "439", "443", "587", "783", "790", "791", "1047", "1355", "1398", "1399", "1866", "1867", "2487", "2491", "3318", "3319", "4199", "4427", "5903", "5911", "7882", "7883", "9959" ]
[ "nonn", "base" ]
52
0
3
[ "A024631", "A244041", "A357425", "A363758" ]
null
Kevin Ryde, Sep 28 2022
2024-04-10T10:45:03
oeisdata/seq/A357/A357425.seq
d45b997496b7c0dc34ae0e563303b316
A357426
Primes p such that p^2+4 is a prime times 5^k for some k >= 1.
[ "11", "19", "31", "41", "61", "71", "79", "89", "109", "131", "139", "149", "151", "181", "191", "239", "241", "251", "379", "389", "409", "421", "461", "499", "509", "541", "599", "631", "659", "661", "709", "719", "769", "811", "919", "1009", "1019", "1021", "1031", "1109", "1129", "1151", "1201", "1231", "1291", "1361", "1399", "1409", "1451", "1489", "1549", "1601", "1621", "1721", "1789", "1871", "1889", "1931", "2011", "2039", "2069", "2131", "2179", "2221", "2251", "2309", "2341", "2351" ]
[ "nonn" ]
17
1
1
[ "A062324", "A357426" ]
null
J. M. Bergot and Robert Israel, Sep 27 2022
2022-10-02T19:14:31
oeisdata/seq/A357/A357426.seq
1e09e475ca5f8163f36d48b740100d02
A357427
Expansion of Product_{k>=0} 1 / (1 + x^Lucas(k)).
[ "1", "-1", "0", "-1", "1", "0", "1", "-2", "2", "-2", "2", "-3", "3", "-2", "4", "-5", "4", "-5", "5", "-5", "6", "-6", "8", "-9", "8", "-9", "9", "-9", "11", "-12", "13", "-14", "14", "-15", "15", "-16", "20", "-20", "20", "-23", "23", "-23", "25", "-28", "31", "-31", "32", "-36", "36", "-36", "41", "-44", "45", "-47", "49", "-52", "54", "-56", "62", "-65", "65", "-69", "72", "-74", "79", "-83", "87", "-91" ]
[ "sign" ]
18
0
8
[ "A000032", "A067595", "A357383", "A357427" ]
null
Ilya Gutkovskiy, Sep 28 2022
2022-09-28T17:30:03
oeisdata/seq/A357/A357427.seq
182e2f8c1ce09e7a59656600484379b8
A357428
Numbers whose digit representation in base 2 is equal to the digit representation in base 2 of the initial terms of their sets of divisors in increasing order.
[ "1", "6", "52", "63", "222", "2037", "6776", "26896", "124641", "220336192", "222066488" ]
[ "nonn", "base", "more" ]
18
1
2
[ "A164894", "A175252", "A357428", "A357429" ]
null
Michel Marcus, Sep 28 2022
2022-10-01T19:18:28
oeisdata/seq/A357/A357428.seq
a0aba451fda10f7eacf249a8f7b17df0
A357429
Numbers whose digit representation in base 3 is equal to the digit representation in base 3 of the initial terms of their sets of divisors in increasing order.
[ "1", "48", "50", "333", "438", "448", "734217", "6561081" ]
[ "nonn", "base", "more" ]
9
1
2
[ "A175252", "A357428", "A357429" ]
null
Michel Marcus, Sep 28 2022
2022-10-02T10:32:23
oeisdata/seq/A357/A357429.seq
aa53aaaa28bfe933edce3ef7a92e98ba
A357430
a(n) is the least integer > 1 such that its digit representation in base n is equal to the digit representation in base n of the initial terms of its set of divisors in increasing order.
[ "6", "48", "6", "182", "8", "66", "10", "102", "12", "1586", "14", "198", "16", "258", "18", "345", "20", "402", "22", "486", "24", "306484", "26", "678", "28", "786", "30", "26102", "32", "1026", "34", "1158", "36", "1335", "38", "1446", "40", "1602", "42", "204741669824", "44", "1938", "46", "2118", "48", "2355", "50", "2502", "52", "2706", "54", "8199524", "56" ]
[ "nonn", "base" ]
17
2
1
[ "A175252", "A357428", "A357429", "A357430" ]
null
Michel Marcus, Sep 28 2022
2022-10-06T04:30:49
oeisdata/seq/A357/A357430.seq
97bbdd46f1e8cd40100248b8d08b22c1
A357431
Triangle read by rows where each term in row n is the next greater multiple of n..1.
[ "1", "2", "3", "3", "4", "5", "4", "6", "8", "9", "5", "8", "9", "10", "11", "6", "10", "12", "15", "16", "17", "7", "12", "15", "16", "18", "20", "21", "8", "14", "18", "20", "24", "27", "28", "29", "9", "16", "21", "24", "25", "28", "30", "32", "33", "10", "18", "24", "28", "30", "35", "36", "39", "40", "41", "11", "20", "27", "32", "35", "36", "40", "44", "45", "46", "47" ]
[ "nonn", "tabl" ]
39
1
2
[ "A007952", "A357417", "A357431", "A357498" ]
null
Tamas Sandor Nagy, Sep 28 2022
2023-05-10T06:25:08
oeisdata/seq/A357/A357431.seq
9207034bd652ac85f7a1599416e84cfb
A357432
a(1) = 1; a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier such that a(n) plus the sum of all previous terms appears in the string concatenation of a(1)..a(n-1).
[ "1", "2", "9", "17", "62", "38", "47", "115", "93", "87", "122", "30", "88", "51", "85", "4", "3", "31", "32", "21", "221", "64", "68", "302", "53", "116", "92", "268", "42", "48", "18", "78", "76", "97", "50", "153", "233", "108", "63", "20", "8", "16", "89", "12", "77", "537", "24", "377", "83", "46", "306", "28", "107", "197", "170", "126", "61", "566", "218", "82", "43", "25", "14", "148", "147", "6", "209", "145", "37", "103" ]
[ "nonn", "base" ]
13
1
2
[ "A000027", "A000217", "A007908", "A337227", "A351753", "A357432", "A357433" ]
null
Scott R. Shannon, Sep 28 2022
2023-01-16T09:10:46
oeisdata/seq/A357/A357432.seq
947f55d9bf79e6d67685872870838dcd
A357433
a(1) = 1; a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier such that the binary string of a(n) plus the sum of all previous terms appears in the binary string concatenation of a(1)..a(n-1).
[ "1", "2", "3", "5", "12", "4", "9", "10", "11", "16", "14", "6", "7", "18", "17", "13", "15", "8", "20", "22", "24", "33", "26", "31", "21", "19", "25", "35", "30", "28", "56", "34", "36", "43", "32", "42", "37", "23", "29", "38", "27", "58", "45", "60", "46", "52", "44", "50", "72", "53", "54", "41", "65", "47", "40", "48", "66", "51", "64", "49", "57", "61", "67", "93", "77", "59", "74", "100", "75", "69", "91", "73", "83", "71", "81", "39", "82" ]
[ "nonn", "base" ]
11
1
2
[ "A000027", "A000217", "A007088", "A007908", "A337227", "A341766", "A357432", "A357433" ]
null
Scott R. Shannon, Sep 28 2022
2023-01-16T09:10:46
oeisdata/seq/A357/A357433.seq
0144320ef973f83dd34bea0f4921e5f4
A357434
a(n) is the number of distinct Q-toothpicks after the n-th stage of the structure described in A211000.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "16", "17", "18", "18", "18", "18", "19", "20", "21", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "22", "23", "24", "25", "26", "27", "28", "28" ]
[ "nonn" ]
24
0
3
[ "A187210", "A211000", "A355479", "A357434" ]
null
Paolo Xausa, Sep 28 2022
2022-10-01T21:15:07
oeisdata/seq/A357/A357434.seq
2d785e6135d5767ea0eddea72ca292da
A357435
a(n) is the least prime p such that p^2+4 is a prime times 5^n.
[ "3", "19", "11", "239", "9011", "61511", "75989", "299011", "4517761", "24830261", "666575989", "2541575989", "41989674011", "147951732239", "455568919739", "174807200989", "9513186107239", "215201662669739", "759834958424011", "5581612302174011", "5404715822825989", "112788443850169739", "2606148434986511" ]
[ "nonn" ]
19
0
1
[ "A357426", "A357435" ]
null
J. M. Bergot and Robert Israel, Sep 28 2022
2023-01-05T18:29:38
oeisdata/seq/A357/A357435.seq
58e25332517e5013ad7cd815e2d4a409
A357436
Start with a(1)=2; to get a(n+1) insert in a(n) the smallest possible digit at the rightmost possible position such that the new number is a prime.
[ "2", "23", "223", "2203", "22003", "220013", "2200103", "22000103", "223000103", "2230001003", "22300010023", "223000100023", "2230001000203", "22301001000203", "223010001000203", "2230010001000203", "22300010001000203", "222300010001000203", "2223000100010001203", "22203000100010001203", "222030001000010001203", "2220300010200010001203" ]
[ "nonn", "base" ]
34
1
1
[ "A125001", "A332603", "A356557", "A357436" ]
null
Bartlomiej Pawlik, Sep 28 2022
2023-06-12T12:33:19
oeisdata/seq/A357/A357436.seq
3789801ea02affc3ef64dfc6cc4d5ab1
A357437
a(1)=0. If there are terms prior to and different from a(n) which have occurred the same number of times as a(n), then a(n+1) = n - m, where a(m) is the most recent occurrence of such a term. If there are no prior terms with the same number of occurrences as a(n), then a(n+1) = n - m, where a(m) is the most recent occurrence of a(n). If a(n) is a first occurrence and no prior term has occurred once only, then a(n+1) = 0
[ "0", "0", "1", "0", "2", "2", "1", "1", "4", "0", "6", "2", "4", "4", "2", "5", "5", "1", "3", "8", "1", "3", "5", "9", "4", "10", "2", "6", "6", "6", "5", "1", "11", "7", "1", "3", "14", "3", "7", "5", "13", "4", "2", "16", "3", "3", "3", "12", "4", "6", "10", "12", "1", "18", "10", "4", "17", "3", "5", "16", "8", "1", "9", "2", "8", "10", "56", "10", "18", "6", "11", "2", "14", "2", "12", "10", "6", "21", "11", "4", "22", "3" ]
[ "nonn" ]
14
1
5
[ "A181391", "A357437" ]
null
Neal Gersh Tolunsky, Sep 28 2022
2022-10-23T19:39:40
oeisdata/seq/A357/A357437.seq
480724c344a9275dbe1e316efa62cc25
A357438
Triangle T(n,k) read by rows, defined by the equation f(x, y) := Sum_{n, k} T(n, k) * y^k * x^n = 1/(1 - x*y - x^2*y*f(x, y+1)).
[ "1", "0", "1", "0", "1", "1", "0", "1", "3", "1", "0", "2", "6", "6", "1", "0", "5", "16", "20", "10", "1", "0", "15", "51", "71", "50", "15", "1", "0", "52", "186", "281", "231", "105", "21", "1", "0", "203", "759", "1223", "1114", "616", "196", "28", "1", "0", "877", "3409", "5795", "5701", "3564", "1428", "336", "36", "1", "0", "4140", "16655", "29634", "31011", "21187", "9780" ]
[ "nonn", "tabl" ]
17
1
9
[ "A000110", "A049347", "A074664", "A357438" ]
null
Michael Somos, Sep 27 2022
2022-09-29T03:50:52
oeisdata/seq/A357/A357438.seq
ed9ae77c635058949fb652edc706c892
A357439
Sums of squares of two odd primes.
[ "18", "34", "50", "58", "74", "98", "130", "146", "170", "178", "194", "218", "242", "290", "298", "314", "338", "370", "386", "410", "458", "482", "530", "538", "554", "578", "650", "698", "722", "818", "850", "866", "890", "962", "970", "986", "1010", "1058", "1082", "1130", "1202", "1250", "1322", "1370", "1378", "1394", "1418", "1490", "1538", "1658", "1682" ]
[ "nonn" ]
7
1
1
[ "A045636", "A103739", "A143850", "A227697", "A357439" ]
null
Giuseppe Melfi, Oct 06 2022
2022-10-10T13:48:21
oeisdata/seq/A357/A357439.seq
75e61c385aeff125f09909c104cd95f9
A357440
Possible half-lengths of self-similar sequences over a finite alphabet that are invariant under retrograde inversion.
[ "3", "11", "15", "23", "35", "36", "39", "44", "51", "63", "75", "83", "95", "99" ]
[ "nonn", "more" ]
3
1
1
[ "A357440", "A357441" ]
null
N. J. A. Sloane, Oct 14 2022
2022-10-14T21:29:15
oeisdata/seq/A357/A357440.seq
f7fce287524eb1ad5d3c2a202efc27fa
A357441
Size of alphabet associated with A357440(n).
[ "2", "2", "6", "2", "2", "8", "2", "8", "2", "18", "10", "2", "2" ]
[ "nonn", "more" ]
7
1
1
[ "A357440", "A357441" ]
null
N. J. A. Sloane, Oct 14 2022
2022-10-14T21:46:35
oeisdata/seq/A357/A357441.seq
39f69786db1325b195aa51079cc30d8a
A357442
Consider a clock face with 2*n "hours" marked around the dial; a(n) = number of ways to match the even hours to the odd hours, modulo rotations and reflections.
[ "1", "1", "3", "5", "17", "53", "260", "1466", "10915", "93196", "917898", "10015299", "119914982", "1557364352", "21797494987", "326930305166", "5230756117008", "88922108947567", "1600594738591550", "30411281088326498", "608225534389576956", "12772735698577492558" ]
[ "nonn" ]
37
1
3
[ "A000031", "A000699", "A007769", "A059375", "A357442" ]
null
N. J. A. Sloane, Nov 06 2022, based on an email from Barry Cipra, Oct 26 2022
2024-02-06T12:59:25
oeisdata/seq/A357/A357442.seq
fb4f72c6abfacb62223d4bac1832ec12
A357443
Inventory sequence, second version: record where the 1's, 2's, etc. are located starting with a(1) = 1, a(2) = 1.
[ "1", "1", "1", "2", "1", "2", "3", "4", "1", "2", "3", "5", "4", "6", "7", "8", "1", "2", "3", "5", "9", "4", "6", "10", "7", "11", "8", "13", "12", "14", "15", "16", "1", "2", "3", "5", "9", "17", "4", "6", "10", "18", "7", "11", "19", "8", "13", "22", "12", "20", "14", "23", "15", "25", "16", "27", "21", "24", "26", "29", "28", "30", "31", "32", "1", "2", "3", "5", "9", "17", "33", "4", "6", "10", "18", "34" ]
[ "nonn", "tabf" ]
16
1
4
[ "A342585", "A356784", "A357443", "A358066" ]
null
Ctibor O. Zizka, Oct 29 2022, edited by N. J. A. Sloane, Nov 07 2022. (Because of a missing term in the initial submission, the definition could be interpreted in two ways: A358066 was the first interpretation, this is the second.)
2022-11-11T09:53:29
oeisdata/seq/A357/A357443.seq
122afa19d8f95a3f9db278c3b8c7ddcf
A357444
Numerators of certain densities associated with partitions into squares.
[ "1", "1", "13", "37", "1", "299", "253", "14113", "317311", "264659" ]
[ "nonn", "frac", "more" ]
9
1
3
[ "A357444", "A357445" ]
null
N. J. A. Sloane, Nov 07 2022
2022-11-08T05:46:32
oeisdata/seq/A357/A357444.seq
42dbc402027ca881947438c9b52d03c3
A357445
Denominators of certain densities associated with partitions into squares.
[ "1", "2", "36", "144", "2", "600", "504", "28224", "635040", "529200" ]
[ "nonn", "frac", "more" ]
10
1
2
[ "A357444", "A357445" ]
null
N. J. A. Sloane, Nov 07 2022
2022-11-08T05:46:47
oeisdata/seq/A357/A357445.seq
5a5809f489a6a3ab1e273c7c7487f8ab
A357446
Number of connected cubic graphs with 2*n nodes and zero edge-Kempe equivalence classes.
[ "0", "0", "0", "2", "5", "34", "212", "1614", "14059", "144712", "1726497", "23550891", "361098825", "6137247735" ]
[ "nonn", "more" ]
10
2
4
[ "A002851", "A357446" ]
null
N. J. A. Sloane, Nov 08 2022
2022-11-13T02:04:22
oeisdata/seq/A357/A357446.seq
5fa4fb427c96f64ecabbcee63cf37f3f
A357447
Number of connected cubic graphs with 2*n nodes and exactly one edge-Kempe equivalence class.
[ "1", "1", "4", "9", "44", "188", "1258", "8917", "75630", "680055", "6496848", "63963867", "644968468", "6606598953" ]
[ "nonn", "more" ]
14
2
3
[ "A002851", "A357447" ]
null
N. J. A. Sloane, Nov 08 2022
2022-11-13T02:04:27
oeisdata/seq/A357/A357447.seq
85d214bff32076db893f1c71b34cb1ab
A357448
Fixed point starting with 0 of the two-block substitution 00->010, 01->010, 10->101, 11->101.
[ "0", "1", "0", "0", "1", "0", "1", "0", "1", "1", "0", "1", "1", "0", "1", "0", "1", "0", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "0", "1", "0", "1", "0", "1", "1", "0", "1", "0", "1", "0", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "1", "0", "1", "1", "0", "1", "0", "1", "0", "1", "0", "1", "1", "0", "1", "0", "1" ]
[ "nonn", "base" ]
17
0
null
[ "A010060", "A244040", "A354896", "A357448" ]
null
Michel Dekking, Sep 29 2022
2023-03-24T15:55:10
oeisdata/seq/A357/A357448.seq
b3c499099bfd9e33d0020f4ca178f304
A357449
a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that the binary string of a(n) plus the largest previous term does not appear in the binary string concatenation of a(0)..a(n-1).
[ "0", "1", "2", "3", "4", "5", "10", "6", "7", "9", "14", "15", "16", "17", "18", "20", "12", "24", "8", "28", "26", "30", "22", "33", "11", "21", "31", "32", "36", "37", "27", "35", "41", "13", "23", "40", "44", "38", "62", "46", "66", "19", "42", "63", "65", "69", "39", "59", "60", "68", "72", "56", "57", "71", "76", "52", "53", "80", "48", "49", "55", "58", "61", "64", "83", "45", "73", "77", "81", "82", "85", "43", "50", "75", "79", "87", "51" ]
[ "nonn", "base", "look" ]
12
0
3
[ "A007088", "A030302", "A118248", "A341766", "A355611", "A357082", "A357449" ]
null
Scott R. Shannon, Sep 29 2022
2023-01-16T09:10:46
oeisdata/seq/A357/A357449.seq
d8f07af53e45e0e022b65be368908984
A357450
a(n) is the smallest integer having exactly n odd square divisors (A298735).
[ "1", "9", "81", "225", "6561", "2025", "531441", "11025", "50625", "164025", "3486784401", "99225", "282429536481", "13286025", "4100625", "893025", "1853020188851841", "2480625", "150094635296999121", "8037225", "332150625", "87169610025", "984770902183611232881", "12006225", "2562890625", "7060738412025", "121550625" ]
[ "nonn" ]
37
1
2
[ "A000290", "A016754", "A038547", "A130279", "A147516", "A298735", "A357450" ]
null
Bernard Schott, Sep 29 2022
2022-10-03T08:45:09
oeisdata/seq/A357/A357450.seq
0ff490160cbf7b4ce2472e6bcbc03d90
A357451
Number of compositions (ordered partitions) of n into tribonacci numbers 1,2,4,7,13,24, ... (A000073).
[ "1", "1", "2", "3", "6", "10", "18", "32", "57", "101", "179", "318", "564", "1002", "1778", "3157", "5603", "9947", "17656", "31342", "55635", "98759", "175308", "311191", "552400", "980571", "1740625", "3089803", "5484750", "9736045", "17282576", "30678512", "54457808", "96668726", "171597851", "304605465", "540708924" ]
[ "nonn" ]
5
0
3
[ "A000073", "A076739", "A117546", "A240844", "A357451", "A357453", "A357455" ]
null
Ilya Gutkovskiy, Sep 29 2022
2022-10-01T00:36:50
oeisdata/seq/A357/A357451.seq
46c4920bbff4b34403dc24fef0addb32
A357452
Number of partitions of n into tetranacci numbers 1,2,4,8,15,29, ... (A000078).
[ "1", "1", "2", "2", "4", "4", "6", "6", "10", "10", "14", "14", "20", "20", "26", "27", "36", "37", "46", "48", "60", "62", "74", "78", "94", "98", "114", "120", "140", "147", "168", "178", "204", "215", "242", "256", "288", "304", "338", "358", "398", "420", "462", "488", "537", "567", "619", "654", "714", "753", "816", "860", "932", "982", "1058", "1114" ]
[ "nonn" ]
5
0
3
[ "A000078", "A003107", "A240844", "A287656", "A357452", "A357453", "A357454" ]
null
Ilya Gutkovskiy, Sep 29 2022
2022-10-01T00:37:02
oeisdata/seq/A357/A357452.seq
e0a767e88be6cefb10e50f64f2651374
A357453
Number of compositions (ordered partitions) of n into tetranacci numbers 1,2,4,8,15,29, ... (A000078).
[ "1", "1", "2", "3", "6", "10", "18", "31", "56", "98", "174", "306", "542", "956", "1690", "2984", "5273", "9313", "16453", "29062", "51340", "90689", "160203", "282994", "499908", "883078", "1559948", "2755624", "4867776", "8598858", "15189770", "26832521", "47399291", "83730207", "147908288", "261277998", "461544073" ]
[ "nonn" ]
5
0
3
[ "A000078", "A076739", "A287656", "A357451", "A357452", "A357453", "A357455" ]
null
Ilya Gutkovskiy, Sep 29 2022
2022-10-01T00:37:09
oeisdata/seq/A357/A357453.seq
a877c3c5080e161ad4a10115bd5a801e
A357454
Number of partitions of n into pentanacci numbers 1,2,4,8,16,31, ... (A001591).
[ "1", "1", "2", "2", "4", "4", "6", "6", "10", "10", "14", "14", "20", "20", "26", "26", "36", "36", "46", "46", "60", "60", "74", "74", "94", "94", "114", "114", "140", "140", "166", "167", "202", "203", "238", "240", "284", "286", "330", "334", "390", "394", "450", "456", "524", "530", "598", "608", "692", "702", "786", "800", "900", "914", "1014", "1034" ]
[ "nonn" ]
5
0
3
[ "A001591", "A003107", "A240844", "A288120", "A357452", "A357454", "A357455" ]
null
Ilya Gutkovskiy, Sep 29 2022
2022-10-01T00:37:16
oeisdata/seq/A357/A357454.seq
4c920cdbfb050eab0298827cf3d77af7
A357455
Number of compositions (ordered partitions) of n into pentanacci numbers 1,2,4,8,16,31, ... (A001591).
[ "1", "1", "2", "3", "6", "10", "18", "31", "56", "98", "174", "306", "542", "956", "1690", "2983", "5272", "9310", "16448", "29050", "51318", "90644", "160118", "282826", "499590", "882468", "1558798", "2753448", "4863696", "8591212", "15175514", "26805984", "47350057", "83639033", "147739853", "260967374", "460972308", "814260589" ]
[ "nonn" ]
5
0
3
[ "A001591", "A076739", "A288120", "A357451", "A357453", "A357454", "A357455" ]
null
Ilya Gutkovskiy, Sep 29 2022
2022-10-01T00:37:23
oeisdata/seq/A357/A357455.seq
10bd0beb537d0d3f33bec034ab64b9b6
A357456
Number of partitions of n into two or more odd parts.
[ "0", "0", "1", "1", "2", "2", "4", "4", "6", "7", "10", "11", "15", "17", "22", "26", "32", "37", "46", "53", "64", "75", "89", "103", "122", "141", "165", "191", "222", "255", "296", "339", "390", "447", "512", "584", "668", "759", "864", "981", "1113", "1259", "1426", "1609", "1816", "2047", "2304", "2589", "2910", "3263", "3658", "4096", "4582", "5119", "5718", "6377", "7108" ]
[ "nonn" ]
5
0
5
[ "A000009", "A000035", "A111133", "A357456", "A357457" ]
null
Ilya Gutkovskiy, Sep 29 2022
2022-10-01T00:37:31
oeisdata/seq/A357/A357456.seq
fde10290f9bd432796bd1b4fb00768ec
A357457
Number of partitions of n into two or more distinct odd parts.
[ "0", "0", "0", "0", "1", "0", "1", "0", "2", "1", "2", "1", "3", "2", "3", "3", "5", "4", "5", "5", "7", "7", "8", "8", "11", "11", "12", "13", "16", "16", "18", "19", "23", "24", "26", "28", "33", "34", "37", "40", "46", "48", "52", "56", "63", "67", "72", "77", "87", "92", "98", "106", "117", "124", "133", "143", "157", "167", "178", "191", "209", "222", "236", "254", "276", "293", "312", "334" ]
[ "nonn" ]
4
0
9
[ "A000035", "A000700", "A357456", "A357457" ]
null
Ilya Gutkovskiy, Sep 29 2022
2022-10-01T00:37:39
oeisdata/seq/A357/A357457.seq
6255f94f6a528c7f8c58b018bec13143
A357458
First differences of A325033 = "Sum of sums of the multiset of prime indices of each prime index of n."
[ "0", "1", "-1", "2", "-1", "1", "-2", "2", "0", "1", "-2", "2", "-1", "1", "-3", "4", "-2", "1", "-1", "1", "0", "1", "-3", "3", "-1", "0", "-1", "2", "-1", "2", "-5", "4", "0", "0", "-2", "2", "-1", "1", "-2", "4", "-3", "2", "-2", "1", "0", "1", "-4", "3", "0", "1", "-2", "1", "-1", "2", "-3", "2", "0", "3", "-4", "2", "0", "-1", "-4", "5", "-1", "4", "-4", "1", "-1", "1", "-3", "4", "-2", "1", "-2", "2" ]
[ "sign" ]
7
1
4
[ "A000720", "A000961", "A001221", "A001222", "A003963", "A005117", "A007716", "A056239", "A109082", "A275024", "A302242", "A302243", "A302505", "A324926", "A325032", "A325033", "A325034", "A357139", "A357187", "A357458" ]
null
Gus Wiseman, Sep 30 2022
2022-10-01T10:25:34
oeisdata/seq/A357/A357458.seq
622dc02cb2d2ed990aa887f64b947339
A357459
The total number of fixed points among all partitions of n, when parts are written in nondecreasing order.
[ "0", "1", "1", "3", "4", "7", "10", "17", "22", "34", "46", "66", "88", "123", "160", "218", "283", "375", "482", "630", "799", "1030", "1299", "1651", "2066", "2602", "3230", "4032", "4976", "6157", "7554", "9288", "11326", "13837", "16793", "20393", "24632", "29763", "35783", "43031", "51527", "61683", "73577", "87729", "104252", "123834", "146664" ]
[ "nonn" ]
14
0
4
[ "A001522", "A099036", "A357459" ]
null
Jeremy Lovejoy, Sep 29 2022
2022-09-30T03:51:00
oeisdata/seq/A357/A357459.seq
c7288246751e84c7d93abb8c7076ff90
A357460
Numbers whose number of deficient divisors is equal to their number of nondeficient divisors.
[ "72", "108", "120", "168", "180", "252", "420", "528", "560", "624", "1188", "1224", "1368", "1400", "1404", "1632", "1656", "1824", "1836", "1960", "1980", "2040", "2052", "2088", "2208", "2232", "2280", "2340", "2484", "2664", "2760", "2772", "2784", "2856", "2952", "2976", "3060", "3096", "3132", "3192", "3200", "3276", "3348", "3384", "3420", "3432" ]
[ "nonn" ]
12
1
1
[ "A000037", "A005101", "A080226", "A335543", "A335544", "A341620", "A357460", "A357461", "A357462" ]
null
Amiram Eldar, Sep 29 2022
2022-09-30T04:25:21
oeisdata/seq/A357/A357460.seq
bb5f5f0ce0c4cd2196ce7c836b0427e8
A357461
Odd numbers whose number of deficient divisors is equal to their number of nondeficient divisors.
[ "3010132125", "4502334375", "5065535475", "6456074625", "8813660625", "9881746875", "15395254875", "15452011575", "16874983125", "18699305625", "19814169375", "19909992375", "21380506875", "25366375125", "26643400875", "26746594875", "28943578125", "31562182575", "33074966925", "34315506225", "35300640375" ]
[ "nonn" ]
10
1
1
[ "A005101", "A005231", "A335543", "A357460", "A357461" ]
null
Amiram Eldar, Sep 29 2022
2022-09-30T04:25:18
oeisdata/seq/A357/A357461.seq
6035d229f8664d2bf6a2dc793fdc3d18
A357462
Numbers whose sum of deficient divisors is equal to their sum of nondeficient divisors.
[ "6", "28", "30", "42", "66", "78", "102", "114", "138", "150", "174", "186", "222", "246", "258", "282", "294", "308", "318", "330", "354", "364", "366", "390", "402", "426", "438", "462", "474", "476", "496", "498", "510", "532", "534", "546", "570", "582", "606", "618", "642", "644", "654", "678", "690", "714", "726", "750", "762", "786", "798", "812", "822", "834" ]
[ "nonn" ]
8
1
1
[ "A000396", "A023196", "A028983", "A187793", "A187794", "A187795", "A335543", "A357460", "A357462" ]
null
Amiram Eldar, Sep 29 2022
2022-09-30T04:25:13
oeisdata/seq/A357/A357462.seq
16f513102d7edd2b45f661a0b979467f
A357463
Decimal expansion of the real root of 2*x^3 + 2*x - 1.
[ "4", "2", "3", "8", "5", "3", "7", "9", "9", "0", "6", "9", "7", "8", "3", "2", "7", "1", "3", "7", "8", "0", "4", "0", "0", "6", "2", "6", "2", "5", "5", "1", "5", "2", "3", "3", "6", "7", "6", "3", "8", "8", "1", "9", "7", "1", "8", "5", "1", "7", "7", "5", "4", "0", "8", "2", "3", "0", "0", "8", "3", "9", "6", "8", "1", "9", "9", "5", "4", "7", "2", "8", "6", "4", "0", "7", "0", "3" ]
[ "nonn", "cons", "easy" ]
7
0
1
[ "A316711", "A357463" ]
null
Wolfdieter Lang, Sep 29 2022
2022-10-13T13:04:40
oeisdata/seq/A357/A357463.seq
b9d562809d9e3dd3375a0c8c7f886f66
A357464
Decimal expansion of the real root of 3*x^3 + x^2 - 1.
[ "5", "9", "8", "1", "9", "3", "4", "9", "8", "1", "1", "0", "8", "5", "5", "3", "3", "0", "4", "2", "7", "8", "3", "7", "9", "0", "6", "2", "1", "0", "0", "4", "9", "4", "4", "6", "7", "3", "3", "9", "8", "4", "2", "4", "7", "1", "5", "0", "5", "6", "1", "0", "6", "8", "0", "3", "2", "3", "5", "9", "8", "9", "0", "5", "1", "1", "0", "3", "4", "9", "8", "8", "1", "2", "4" ]
[ "nonn", "cons", "easy" ]
9
0
1
[ "A357464", "A357465" ]
null
Wolfdieter Lang, Sep 30 2022
2022-11-09T05:00:39
oeisdata/seq/A357/A357464.seq
7858ab95dbd4b89c3b9a0f5dd84a420d
A357465
Decimal expansion of the real root of 3*x^3 - x^2 - 1.
[ "8", "2", "4", "1", "2", "2", "6", "2", "1", "1", "0", "9", "1", "3", "2", "9", "6", "6", "3", "1", "2", "2", "7", "8", "9", "7", "9", "8", "7", "0", "2", "8", "2", "5", "6", "2", "6", "4", "3", "3", "2", "6", "4", "1", "4", "3", "7", "0", "6", "3", "8", "7", "2", "8", "9", "1", "6", "0", "4", "3", "7", "6", "5", "4", "2", "0", "9", "7", "8", "0", "9", "8", "6", "8", "1", "2" ]
[ "nonn", "cons", "easy" ]
9
0
1
[ "A357464", "A357465" ]
null
Wolfdieter Lang, Sep 30 2022
2022-11-09T05:02:08
oeisdata/seq/A357/A357465.seq
caa9b8cbf12e111aed9551bb6eb6d320
A357466
Decimal expansion of the real root of 3*x^3 - x - 1.
[ "8", "5", "1", "3", "8", "3", "0", "7", "2", "8", "6", "6", "9", "2", "4", "3", "9", "3", "4", "9", "3", "9", "4", "0", "1", "1", "2", "1", "8", "7", "8", "5", "9", "3", "8", "5", "0", "9", "6", "1", "4", "9", "9", "2", "3", "9", "3", "8", "0", "4", "1", "9", "6", "5", "0", "5", "9", "0", "0", "2", "3", "9", "6", "2", "7", "9", "7", "2", "2", "5", "5", "3", "0", "4", "5", "7", "2", "4", "8", "6", "5", "8", "6", "9", "6" ]
[ "nonn", "cons", "easy" ]
10
0
1
[ "A357465", "A357466", "A357467" ]
null
Wolfdieter Lang, Oct 17 2022
2022-12-29T06:23:42
oeisdata/seq/A357/A357466.seq
eb9c3f60da98b494382159cafa87b857
A357467
Decimal expansion of the real root of 3*x^3 + x - 1.
[ "5", "3", "6", "5", "6", "5", "1", "6", "4", "6", "7", "2", "2", "2", "2", "9", "1", "8", "7", "5", "7", "4", "2", "4", "5", "1", "2", "2", "3", "8", "7", "7", "3", "8", "3", "3", "8", "2", "1", "2", "4", "2", "2", "6", "3", "7", "5", "2", "1", "8", "8", "0", "6", "6", "3", "1", "4", "2", "3", "7", "1", "5", "1", "4", "2", "0", "6", "7", "0", "1", "1", "2", "4", "5", "4", "8" ]
[ "nonn", "cons", "easy" ]
10
0
1
[ "A357464", "A357466", "A357467" ]
null
Wolfdieter Lang, Oct 17 2022
2025-03-23T20:53:25
oeisdata/seq/A357/A357467.seq
76b1545dc310f1a8b052cf09f078a7cd
A357468
Decimal expansion of the real root of x^3 + x^2 + x - 2.
[ "8", "1", "0", "5", "3", "5", "7", "1", "3", "7", "6", "6", "1", "3", "6", "7", "7", "4", "0", "2", "1", "2", "5", "1", "4", "1", "4", "3", "2", "5", "6", "6", "8", "2", "1", "4", "1", "0", "7", "2", "6", "1", "4", "9", "0", "0", "0", "0", "5", "3", "0", "2", "4", "7", "4", "4", "3", "0", "9", "7", "6", "7", "4", "5", "0", "9", "4", "5", "9", "4", "0", "8", "7", "4", "7", "2" ]
[ "nonn", "cons", "easy" ]
10
0
1
[ "A137421", "A357468" ]
null
Wolfdieter Lang, Oct 17 2022
2022-12-15T17:01:34
oeisdata/seq/A357/A357468.seq
b3a01b53f73e9c26c27f8c8f3b984b86
A357469
Decimal expansion of the real root of x^3 - x^2 + x - 2.
[ "1", "3", "5", "3", "2", "0", "9", "9", "6", "4", "1", "9", "9", "3", "2", "4", "4", "2", "9", "4", "8", "3", "1", "0", "1", "3", "3", "2", "5", "7", "7", "3", "8", "8", "4", "5", "7", "2", "7", "0", "7", "0", "5", "6", "1", "3", "8", "5", "6", "8", "4", "6", "8", "2", "6", "8", "0", "6", "6", "9", "3", "0", "4", "2", "6", "5", "1", "5", "1", "8", "9", "7", "2", "3", "2", "2", "0", "9", "2", "0", "8", "5", "9", "1", "6", "5", "8", "0", "3", "9", "7", "7" ]
[ "nonn", "cons", "easy" ]
18
1
2
[ "A137421", "A197032", "A357468", "A357469" ]
null
Wolfdieter Lang, Oct 17 2022
2023-08-14T10:33:44
oeisdata/seq/A357/A357469.seq
319519023f44067137b7f5c67626ff21
A357470
Decimal expansion of the real root of x^3 - x^2 - 2*x - 1.
[ "2", "1", "4", "7", "8", "9", "9", "0", "3", "5", "7", "0", "4", "7", "8", "7", "3", "5", "4", "0", "2", "6", "2", "1", "4", "9", "6", "4", "9", "3", "0", "9", "8", "7", "3", "6", "4", "9", "1", "6", "7", "6", "6", "1", "5", "0", "3", "7", "0", "2", "8", "4", "2", "7", "9", "4", "4", "6", "9", "1", "1", "7", "1", "7", "8", "8", "9", "1", "5", "9", "6", "7", "5", "3", "7", "2", "0", "1" ]
[ "nonn", "cons", "easy" ]
17
1
1
[ "A160389", "A255249", "A255524", "A357470", "A357471", "A357472" ]
null
Wolfdieter Lang, Oct 25 2022
2022-11-14T05:58:50
oeisdata/seq/A357/A357470.seq
dd8b7f7a651678364bcc32dd32d1341b
A357471
Decimal expansion of the real root of x^3 - x^2 + 2*x - 1.
[ "5", "6", "9", "8", "4", "0", "2", "9", "0", "9", "9", "8", "0", "5", "3", "2", "6", "5", "9", "1", "1", "3", "9", "9", "9", "5", "8", "1", "1", "9", "5", "6", "8", "6", "4", "8", "8", "3", "9", "7", "9", "7", "4", "3", "9", "1", "2", "8", "9", "4", "0", "2", "2", "0", "5", "4", "4", "7", "3", "1", "0", "7", "9", "6", "5", "6", "7", "4", "7", "1", "9", "6", "1", "1", "7", "4", "6", "6" ]
[ "nonn", "cons", "easy" ]
12
0
1
[ "A160389", "A255249", "A255524", "A357470", "A357471", "A357472" ]
null
Wolfdieter Lang, Oct 25 2022
2022-11-09T05:10:53
oeisdata/seq/A357/A357471.seq
f2b851fbb1a22dc096333d38aee5f1dc
A357472
Decimal expansion of the real root of x^3 + x^2 + 2*x - 1.
[ "3", "9", "2", "6", "4", "6", "7", "8", "1", "7", "0", "2", "6", "4", "0", "8", "1", "1", "7", "6", "4", "8", "7", "9", "5", "9", "4", "8", "8", "4", "3", "4", "1", "2", "5", "0", "7", "0", "3", "7", "6", "4", "9", "6", "8", "5", "9", "3", "4", "8", "2", "5", "8", "9", "7", "3", "1", "1", "3", "9", "6", "4", "9", "8", "4", "4", "5", "1", "7", "1", "6", "6", "8", "4", "7", "0", "8" ]
[ "nonn", "cons", "easy" ]
16
0
1
[ "A160389", "A255249", "A255524", "A357470", "A357471", "A357472" ]
null
Wolfdieter Lang, Oct 25 2022
2022-11-09T05:13:09
oeisdata/seq/A357/A357472.seq
c5b2d274ed39059807b321c193f6fd97
A357473
Number of types of generalized symmetries in diagonal Latin squares of order n.
[ "1", "0", "0", "10", "8", "12", "12" ]
[ "nonn", "more", "hard" ]
41
1
4
[ "A000041", "A274171", "A287649", "A287650", "A293777", "A357473", "A358394", "A358515", "A358891" ]
null
Eduard I. Vatutin, Sep 29 2022
2023-05-03T23:29:06
oeisdata/seq/A357/A357473.seq
6e5dcd75e670ac74c43268bfcfe061d8
A357474
Squarely correct numbers.
[ "1", "4", "9", "11", "14", "16", "19", "25", "36", "41", "44", "49", "64", "81", "91", "94", "99", "100", "111", "114", "116", "119", "121", "125", "136", "141", "144", "149", "161", "164", "169", "181", "191", "194", "196", "199", "225", "251", "254", "256", "259", "289", "324", "361", "364", "369", "400", "411", "414", "416", "419", "425", "436", "441", "444", "449", "464" ]
[ "nonn", "easy", "base" ]
20
1
2
[ "A000290", "A018851", "A036435", "A357474" ]
null
Freddy Barrera, Sep 29 2022
2022-11-19T03:28:30
oeisdata/seq/A357/A357474.seq
15d78d735af75397ed7981ee9f8bbffc
A357475
Expansion of Product_{k>=1} 1 / (1 + x^k)^Fibonacci(k).
[ "1", "-1", "0", "-2", "0", "-3", "0", "-4", "2", "-5", "8", "0", "26", "19", "74", "74", "195", "221", "464", "560", "1042", "1258", "2154", "2536", "3997", "4341", "6152", "5204", "5447", "-1617", "-10790", "-39710", "-83915", "-181639", "-336564", "-633844", "-1108334", "-1952371", "-3293590", "-5568202", "-9148916", "-15017471", "-24144556", "-38697396", "-61005748", "-95708150" ]
[ "sign" ]
15
0
4
[ "A000045", "A166861", "A261050", "A337009", "A357179", "A357475" ]
null
Ilya Gutkovskiy, Oct 02 2022
2023-04-30T15:45:04
oeisdata/seq/A357/A357475.seq
66077bf986f5d70406ae25f9b7fa6855
A357476
Number of partitions of n into two or more powers of 2.
[ "0", "0", "1", "2", "3", "4", "6", "6", "9", "10", "14", "14", "20", "20", "26", "26", "35", "36", "46", "46", "60", "60", "74", "74", "94", "94", "114", "114", "140", "140", "166", "166", "201", "202", "238", "238", "284", "284", "330", "330", "390", "390", "450", "450", "524", "524", "598", "598", "692", "692", "786", "786", "900", "900", "1014", "1014", "1154", "1154", "1294", "1294", "1460" ]
[ "nonn" ]
13
0
4
[ "A000065", "A018819", "A209229", "A357476", "A357534" ]
null
Ilya Gutkovskiy, Oct 02 2022
2022-10-08T14:23:13
oeisdata/seq/A357/A357476.seq
93394a814d6bbb58d322f3848095f312
A357477
a(n) is the smallest k such that the square root of k*n rounds to a prime.
[ "3", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "3", "3", "3", "6", "6", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "4", "4", "4", "5", "5", "5", "3", "3", "3", "3", "3", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "8", "8", "4", "4", "4", "4", "4", "4", "4", "4", "7", "7", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "3", "3", "3", "3" ]
[ "nonn", "easy" ]
34
1
1
[ "A357477", "A357675", "A357676" ]
null
Jake M. Gotlieb, Sep 30 2022
2022-10-19T13:40:21
oeisdata/seq/A357/A357477.seq
b54773474efbcd80e766a5d7b23ae47e
A357478
Numbers n such that both n and n+1 are in A175729.
[ "7105", "37583", "229177", "309281", "343865", "480654", "794625", "808860", "977185", "2135895", "2174080", "2755841", "5978490", "6865055", "7147761", "8784216", "11207889", "15251713", "15854166", "21526897", "28432040", "29831601", "32865300", "33531212", "40931731", "53237184", "57766731", "63564985", "67849950", "70751360", "72352760", "85121596" ]
[ "nonn" ]
14
1
1
[ "A175729", "A357478" ]
null
J. M. Bergot and Robert Israel, Sep 30 2022
2022-10-02T10:33:17
oeisdata/seq/A357/A357478.seq
f46297ac88a6877f72ff36bef0e0b83a
A357479
a(n) = (n!/6) * Sum_{k=0..n-3} 1/k!.
[ "0", "0", "0", "1", "8", "50", "320", "2275", "18256", "164388", "1644000", "18084165", "217010200", "2821132886", "39495860768", "592437911975", "9479006592160", "161143112067400", "2900576017214016", "55110944327067273", "1102218886541346600", "23146596617368279930", "509225125582102160000" ]
[ "nonn", "easy" ]
26
0
5
[ "A000292", "A000449", "A000522", "A007526", "A038155", "A073107", "A357479", "A357480" ]
null
Seiichi Manyama, Sep 30 2022
2023-04-02T14:24:48
oeisdata/seq/A357/A357479.seq
95b6d3a2ba21b0c684d066f6119b1845
A357480
a(n) = (n!/24) * Sum_{k=0..n-4} 1/k!.
[ "0", "0", "0", "0", "1", "10", "75", "560", "4550", "41076", "410970", "4521000", "54252495", "705283150", "9873965101", "148109477880", "2369751647900", "40285778016680", "725144004303300", "13777736081766576", "275554721635336365", "5786649154342069650", "127306281395525539615", "2928044472097087420000" ]
[ "nonn", "easy" ]
18
0
6
[ "A000332", "A000475", "A000522", "A007526", "A038155", "A073107", "A357479", "A357480" ]
null
Seiichi Manyama, Sep 30 2022
2022-10-01T02:06:38
oeisdata/seq/A357/A357480.seq
f68678020d7b610af676912d2d2da52e
A357481
a(n) is the least integer b such that the digit representation of n in base b is equal to the digit representation in base b of the initial terms of the sets of divisors of n in increasing order, or -1 if no such b exists.
[ "2", "-1", "-1", "-1", "-1", "2", "-1", "6", "6", "8", "-1", "10", "-1", "12", "12", "14", "-1", "16", "-1", "18", "18", "20", "-1", "22", "20", "24", "24", "26", "-1", "28", "-1", "30", "30", "32", "30", "34", "-1", "36", "36", "38", "-1", "40", "-1", "42", "42", "44", "-1", "3", "42", "3", "48", "2", "-1", "52", "50", "54", "54", "56", "-1", "58", "-1", "60", "2", "62", "60", "7", "-1", "66", "66", "68", "-1", "70", "-1", "72", "7" ]
[ "sign", "base" ]
23
1
1
[ "A056653", "A175252", "A357428", "A357429", "A357481" ]
null
Michel Marcus, Sep 30 2022
2022-10-06T04:30:54
oeisdata/seq/A357/A357481.seq
87b81bc93dd552b3dafd0cac0b3329f2
A357482
a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that the binary string of the number of 1's in the binary value of a(n) + the number of 1's in the binary values of all previous terms does not appear in the binary string concatenation of a(0)..a(n-1).
[ "0", "1", "2", "3", "7", "4", "5", "63", "8", "6", "9", "16", "127", "11", "10", "12", "13", "14", "19", "511", "1023", "15", "21", "17", "31", "18", "20", "22", "24", "25", "33", "23", "27", "26", "28", "35", "37", "38", "41", "1535", "29", "30", "32", "34", "47", "36", "40", "55", "39", "43", "42", "45", "255", "46", "51", "383", "48", "44", "4095", "64", "447", "65", "95", "53", "191", "767", "1791", "59", "49", "54", "57", "50", "52" ]
[ "nonn", "base" ]
9
0
3
[ "A007088", "A030302", "A118248", "A355611", "A357082", "A357449", "A357482" ]
null
Scott R. Shannon, Sep 30 2022
2023-01-16T09:10:46
oeisdata/seq/A357/A357482.seq
be3bfc4a5cd67d58ca37d6e254da667d
A357483
Decimal expansion of sum of squares of reciprocals of primes whose distance to the next prime is equal to 6, Sum_{j>=1} 1/A031924(j)^2.
[ "0", "0", "4", "7", "5", "7", "2", "8", "6", "9", "7", "5" ]
[ "nonn", "cons", "hard", "more" ]
13
0
3
[ "A031924", "A085548", "A160910", "A242301", "A356793", "A357059", "A357483" ]
null
Artur Jasinski, Sep 30 2022
2022-10-02T00:27:46
oeisdata/seq/A357/A357483.seq
69074accca8a7899f30f79c35590ec10
A357484
Number of linearity regions of a max-pooling function with a 3 by n input and 2 by 2 pooling windows.
[ "1", "14", "150", "1536", "15594", "158050", "1601356", "16223814", "164366170", "1665216896", "16870539234", "170917714410", "1731590444316", "17542976546494", "177730263461890", "1800609290091936", "18242215773029194", "184814350419581330", "1872379131238643436", "18969325721395559574" ]
[ "nonn", "easy" ]
26
1
2
[ "A007070", "A033303", "A357484" ]
null
Alejandro H. Morales, Sep 30 2022
2022-10-06T16:26:40
oeisdata/seq/A357/A357484.seq
288b1f1c51c44fa1f9a155a8b6d221bf
A357485
Heinz numbers of integer partitions with the same length as reverse-alternating sum.
[ "1", "2", "20", "42", "45", "105", "110", "125", "176", "182", "231", "245", "312", "374", "396", "429", "494", "605", "663", "680", "702", "780", "782", "845", "891", "969", "1064", "1088", "1100", "1102", "1311", "1426", "1428", "1445", "1530", "1755", "1805", "1820", "1824", "1950", "2001", "2024", "2146", "2156", "2394", "2448", "2475", "2508", "2542" ]
[ "nonn" ]
6
1
2
[ "A000009", "A000041", "A000712", "A001055", "A004526", "A006330", "A025047", "A051159", "A131044", "A262046", "A301987", "A349159", "A349160", "A357136", "A357182", "A357184", "A357189", "A357485", "A357486", "A357487" ]
null
Gus Wiseman, Oct 01 2022
2022-10-02T10:33:45
oeisdata/seq/A357/A357485.seq
a539fe3e4cf6e134767f1604b4b01722
A357486
Heinz numbers of integer partitions with the same length as alternating sum.
[ "1", "2", "10", "20", "21", "42", "45", "55", "88", "91", "105", "110", "125", "156", "176", "182", "187", "198", "231", "245", "247", "312", "340", "351", "374", "390", "391", "396", "429", "494", "532", "544", "550", "551", "605", "663", "680", "702", "713", "714", "765", "780", "782", "845", "891", "910", "912", "969", "975", "1012", "1064", "1073", "1078" ]
[ "nonn" ]
6
1
2
[ "A000009", "A000041", "A000712", "A001055", "A004526", "A006330", "A025047", "A051159", "A131044", "A262046", "A301987", "A349159", "A349160", "A357136", "A357182", "A357184", "A357189", "A357486", "A357487" ]
null
Gus Wiseman, Oct 01 2022
2022-10-02T10:33:39
oeisdata/seq/A357/A357486.seq
0b399cb4765d4aa8740fd20a1aadf1af
A357487
Number of integer partitions of n with the same length as reverse-alternating sum.
[ "1", "1", "0", "0", "0", "1", "0", "2", "0", "4", "0", "5", "0", "9", "0", "13", "0", "23", "0", "34", "0", "54", "0", "78", "0", "120", "0", "170", "0", "252", "0", "358", "0", "517", "0", "725", "0", "1030", "0", "1427", "0", "1992", "0", "2733", "0", "3759", "0", "5106", "0", "6946", "0", "9345", "0", "12577", "0", "16788", "0", "22384", "0", "29641", "0" ]
[ "nonn" ]
5
0
8
[ "A000009", "A000041", "A001055", "A004526", "A025047", "A051159", "A097805", "A103919", "A114220", "A131044", "A262046", "A262977", "A301987", "A335405", "A344651", "A357136", "A357182", "A357183", "A357184", "A357189", "A357485", "A357486", "A357487", "A357488" ]
null
Gus Wiseman, Oct 01 2022
2022-10-02T10:33:35
oeisdata/seq/A357/A357487.seq
a063002e2caf74e764201267b3ed3e12
A357488
Number of integer partitions of 2n - 1 with the same length as alternating sum.
[ "1", "0", "1", "2", "4", "5", "9", "13", "23", "34", "54", "78", "120", "170", "252", "358", "517", "725", "1030", "1427", "1992", "2733", "3759", "5106", "6946", "9345", "12577", "16788", "22384", "29641", "39199", "51529", "67626", "88307", "115083", "149332", "193383", "249456", "321134", "411998", "527472", "673233", "857539", "1089223", "1380772" ]
[ "nonn" ]
11
1
4
[ "A000009", "A000041", "A001055", "A004526", "A025047", "A051159", "A097805", "A103919", "A114220", "A131044", "A222763", "A262046", "A262977", "A335405", "A344651", "A357136", "A357182", "A357183", "A357184", "A357189", "A357485", "A357486", "A357487", "A357488" ]
null
Gus Wiseman, Oct 02 2022
2022-10-04T08:40:18
oeisdata/seq/A357/A357488.seq
b22638bb221d8ad0c9e4bcdaef34ae9e
A357489
Numbers k such that the k-th composition in standard order is a triple (w,x,y) such that 2w = 3x + 4y.
[ "133", "1034", "4113", "8212", "32802", "65576", "131137", "262212", "524368", "1048706", "2097288", "4194464", "4194561", "8388868", "16777488", "33554752", "33554946", "67109384", "134218272", "134218753", "268436096", "268436484", "536871952", "1073742912", "1073743874", "2147484928", "2147485704", "4294969376" ]
[ "nonn" ]
11
1
1
[ "A000120", "A008676", "A011782", "A029837", "A029931", "A066099", "A070939", "A133494", "A357489", "A357849", "A358102" ]
null
Gus Wiseman, Nov 02 2022
2022-11-03T05:41:43
oeisdata/seq/A357/A357489.seq
452de868f10fed275d3b39558e12196c
A357490
Numbers k such that the k-th composition in standard order has integer geometric mean.
[ "1", "2", "3", "4", "7", "8", "10", "15", "16", "17", "24", "31", "32", "36", "42", "63", "64", "69", "70", "81", "88", "98", "104", "127", "128", "136", "170", "255", "256", "277", "278", "282", "292", "325", "326", "337", "344", "354", "360", "394", "418", "424", "511", "512", "513", "514", "515", "528", "547", "561", "568", "640", "682", "768", "769", "785", "792", "896" ]
[ "nonn" ]
5
1
2
[ "A051293", "A067538", "A067539", "A078174", "A078175", "A096199", "A102627", "A271654", "A301987", "A320322", "A326027", "A326028", "A326567", "A326568", "A326622", "A326623", "A326624", "A326625", "A326641", "A326645", "A335405", "A339452", "A357184", "A357490", "A357710" ]
null
Gus Wiseman, Oct 16 2022
2022-10-17T07:07:27
oeisdata/seq/A357/A357490.seq
7f697e1acf3b805091ae8407dceb9f8a
A357491
Distinct values in A356784, in order of appearance.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "11", "13", "14", "15", "16", "17", "18", "21", "19", "22", "24", "26", "20", "23", "25", "28", "27", "29", "30", "31", "32", "33", "34", "38", "35", "39", "42", "45", "36", "40", "43", "48", "46", "50", "52", "54", "37", "41", "44", "49", "56", "47", "51", "57", "53", "58", "55", "60", "59", "61", "62", "63", "64", "65", "66", "71" ]
[ "nonn" ]
12
0
3
[ "A356784", "A357491", "A357492" ]
null
Rémy Sigrist, Oct 01 2022
2022-10-02T10:53:14
oeisdata/seq/A357/A357491.seq
028077188e7b5e541b23fca8116943c3
A357492
Inverse permutation to A357491.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "11", "13", "14", "15", "16", "17", "18", "20", "24", "19", "21", "25", "22", "26", "23", "28", "27", "29", "30", "31", "32", "33", "34", "36", "40", "48", "35", "37", "41", "49", "38", "42", "50", "39", "44", "53", "43", "51", "45", "54", "46", "56", "47", "58", "52", "55", "57", "60", "59", "61", "62", "63", "64", "65", "66", "68" ]
[ "nonn" ]
10
0
3
[ "A356784", "A357491", "A357492" ]
null
Rémy Sigrist, Oct 01 2022
2022-10-02T10:53:18
oeisdata/seq/A357/A357492.seq
4bc08a1c6108e698e75021c4520ec870
A357493
Numbers k such that s(k) = 3*k, where s(k) is the sum of divisors of k that have a square factor (A162296).
[ "480", "2688", "56304", "89400", "195216", "2095104", "9724032", "69441408", "1839272960", "5905219584" ]
[ "nonn", "more" ]
9
1
1
[ "A001248", "A005117", "A005820", "A013929", "A068403", "A162296", "A322609", "A325314", "A357493", "A357494" ]
null
Amiram Eldar, Oct 01 2022
2022-10-01T19:29:48
oeisdata/seq/A357/A357493.seq
ce95553332e5abf6521087a464289538
A357494
Numbers k such that s(k) = 4*k, where s(k) is the sum of divisors of k that have a square factor (A162296).
[ "902880", "1534680", "361674720", "767685600", "4530770640", "4941414720", "5405788800", "5517818880", "16993944000", "20429240832", "94820077440" ]
[ "nonn", "more" ]
5
1
1
[ "A001248", "A005117", "A013929", "A023198", "A027687", "A162296", "A322609", "A325314", "A357493", "A357494" ]
null
Amiram Eldar, Oct 01 2022
2022-10-01T19:29:57
oeisdata/seq/A357/A357494.seq
c0f95670d8320bd983ac5bf45beaef18
A357495
Lesser of a pair of amicable numbers k < m such that s(k) = m and s(m) = k, where s(k) = A162296(k) - k is the sum of aliquot divisors of k that have a square factor.
[ "880", "10480", "20080", "24928", "42976", "69184", "110565", "252080", "267712", "489472", "566656", "569240", "603855", "626535", "631708", "687424", "705088", "741472", "786896", "904365", "1100385", "1234480", "1280790", "1425632", "1749824", "1993750", "2012224", "2401568", "2439712", "2496736", "2542496", "2573344", "2671856" ]
[ "nonn" ]
10
1
1
[ "A002025", "A002952", "A013929", "A126165", "A126169", "A162296", "A259038", "A292980", "A322541", "A322609", "A324708", "A325314", "A348343", "A357493", "A357494", "A357495", "A357496" ]
null
Amiram Eldar, Oct 01 2022
2022-10-03T04:09:59
oeisdata/seq/A357/A357495.seq
bfc6baeb9e30f56449f89301961315b6
A357496
Greater of a pair of amicable numbers k < m such that s(k) = m and s(m) = k, where s(k) = A162296(k) - k is the sum of aliquot divisors of k that have a square factor.
[ "1136", "11696", "22256", "25472", "43424", "73664", "131355", "304336", "267968", "492608", "612704", "674920", "640305", "788697", "691292", "705344", "723392", "813728", "809776", "1117395", "1258335", "1559696", "1518570", "1598368", "1821376", "2218250", "2058944", "2678752", "2744288", "2765024", "2848864", "2610656", "3134224" ]
[ "nonn" ]
12
1
1
[ "A002046", "A002953", "A013929", "A126166", "A126170", "A162296", "A259039", "A292981", "A322542", "A322609", "A324709", "A325314", "A348344", "A357493", "A357494", "A357495", "A357496" ]
null
Amiram Eldar, Oct 01 2022
2022-10-03T04:11:09
oeisdata/seq/A357/A357496.seq
6ed39697d34dac8ce4e1a2a388d234e1
A357497
Nonsquarefree numbers whose harmonic mean of nonsquarefree divisors in an integer.
[ "4", "9", "12", "18", "24", "25", "28", "45", "49", "54", "60", "90", "112", "121", "126", "132", "150", "153", "168", "169", "198", "270", "289", "294", "336", "361", "364", "414", "529", "560", "594", "630", "637", "684", "726", "841", "918", "961", "1014", "1140", "1232", "1305", "1350", "1369", "1512", "1521", "1638", "1680", "1681", "1710", "1734", "1849", "1984" ]
[ "nonn" ]
9
1
1
[ "A001248", "A001599", "A006086", "A013929", "A063947", "A162296", "A286325", "A319745", "A322609", "A335387", "A357493", "A357494", "A357495", "A357496", "A357497" ]
null
Amiram Eldar, Oct 01 2022
2022-10-03T04:16:49
oeisdata/seq/A357/A357497.seq
81c1d09bc390d36b13153f9ea7557162
A357498
Triangle read by rows where each term in row n is the next greater multiple of n..1 divided by n..1.
[ "1", "1", "3", "1", "2", "5", "1", "2", "4", "9", "1", "2", "3", "5", "11", "1", "2", "3", "5", "8", "17", "1", "2", "3", "4", "6", "10", "21", "1", "2", "3", "4", "6", "9", "14", "29", "1", "2", "3", "4", "5", "7", "10", "16", "33", "1", "2", "3", "4", "5", "7", "9", "13", "20", "41", "1", "2", "3", "4", "5", "6", "8", "11", "15", "23", "47", "1", "2", "3", "4", "5", "6", "8", "10", "13", "18", "28", "57" ]
[ "nonn", "tabl", "easy" ]
42
1
3
[ "A007952", "A357431", "A357498", "A358435" ]
null
Tamas Sandor Nagy, Oct 01 2022
2023-05-10T07:28:21
oeisdata/seq/A357/A357498.seq
843da643bb3a67c9e08e56234eb0e099
A357499
Triangle read by rows: T(n,k) is the length of the longest induced path in the n-dimensional hypercube, such that the end points of the path are at Hamming distance k, 0 <= k <= n.
[ "0", "0", "1", "0", "1", "2", "0", "1", "4", "3", "0", "1", "6", "7", "4", "0", "1", "12", "13", "12", "11", "0", "1", "26", "25", "24", "25", "24" ]
[ "nonn", "tabl", "more", "hard" ]
7
0
6
[ "A099155", "A357360", "A357499" ]
null
Pontus von Brömssen, Oct 01 2022
2022-10-02T08:34:07
oeisdata/seq/A357/A357499.seq
ab92fbffc4b49c42ac77c7647054160b
A357500
Largest number of nodes of an induced path in the n X n knight graph.
[ "1", "1", "7", "9", "15", "21", "24", "34" ]
[ "nonn", "more" ]
23
1
3
[ "A165143", "A331968", "A357500" ]
null
Pontus von Brömssen, Oct 01 2022
2023-01-31T01:13:15
oeisdata/seq/A357/A357500.seq
405f4e4a9f8119d0f8468c9f829d1914