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 A249306 Denominators A027642(n) of Bernoulli numbers except for a(4*k+5)=2 instead of 1. 1
 1, 2, 6, 1, 30, 2, 42, 1, 30, 2, 66, 1, 2730, 2, 6, 1, 510, 2, 798, 1, 330, 2, 138, 1, 2730, 2, 6, 1, 870, 2, 14322, 1, 510, 2, 6, 1, 1919190, 2, 6, 1, 13530, 2, 1806, 1, 690, 2, 282, 1, 46410, 2, 66, 1, 1590, 2, 798, 1, 870, 2, 354, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS There exist an infinity of 1's, 2's, 6's, 30's, 42's, 66's, ... . Respective ranks: 0, 3, 7, 11, 15, 19, ... 1, 5, 9, 13, 17, 21, ... (= A016813) 2, 14, 26, 34, 38, 62, ... (= A051222) 4, 8, 68, 76, 124, 152, ... (= A051226) 6, 114, 186, 258, 354, 402, ... (= A051228) 10, 50, 170, 370, 470, 590, ... (= A051230) 12, 24, 1308, 1884, 2004, 2364, ... (= A249134) etc. Hence by antidiagonals a permutation of A001477(n). First column: A248614(n). a(n) is an alternative sequence for the denominators of the Bernoulli numbers. First 36 terms of the corresponding clockwise spiral: . 330------2----138------1---2730------2 | | | | 1 42------1-----30------2 6 | | | | | | | | 798 2 1------2 66 1 | | | | | | | | | | 2 30------1------6 1 870 | | | | | | 510------1------6------2---2730 2 | | 1------6------2----510------1--14322 LINKS Table of n, a(n) for n=0..59. Index entries for sequences related to Bernoulli numbers FORMULA a(2n) = A002445(n), a(2n+1) = A000034(n+1). MAPLE Clausen := proc(n) local S, i; S := numtheory[divisors](n); S := map(i->i+1, S); S := select(isprime, S); mul(i, i=S) end: A249306 := n -> `if`(n mod 4 = 3, 1, Clausen(n)): seq(A249306(n), n=0..59); # Peter Luschny, Nov 10 2014 MATHEMATICA a[n_] := Denominator[BernoulliB[n]]; a[n_ /; Mod[n, 4] == 1] = 2; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Oct 28 2014 *) CROSSREFS A variant of the Clausen numbers A141056, A160014. And of A176591. Cf. A000034, A002445, A016813, A027642, A051222, A051226, A051228, A051230, A090126, A164020, A248614, A249134. Sequence in context: A366427 A366571 A027642 * A347427 A117214 A185972 Adjacent sequences: A249303 A249304 A249305 * A249307 A249308 A249309 KEYWORD nonn AUTHOR Paul Curtz, Oct 28 2014 STATUS approved

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Last modified May 20 05:07 EDT 2024. Contains 372703 sequences. (Running on oeis4.)