cp's OEIS Frontend

A249306 Denominators A027642(n) of Bernoulli numbers except for a(4*k+5)=2 instead of 1.

%I A249306 #52 Aug 17 2018 21:31:06
%S A249306 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,
%T A249306 2,6,1,870,2,14322,1,510,2,6,1,1919190,2,6,1,13530,2,1806,1,690,2,282,
%U A249306 1,46410,2,66,1,1590,2,798,1,870,2,354,1
%N A249306 Denominators A027642(n) of Bernoulli numbers except for a(4*k+5)=2 instead of 1.
%C A249306 There exist an infinity of 1's, 2's, 6's, 30's, 42's, 66's, ... .
%C A249306 Respective ranks:
%C A249306    0,   3,    7,   11,   15,   19, ...
%C A249306    1,   5,    9,   13,   17,   21, ...   (= A016813)
%C A249306    2,  14,   26,   34,   38,   62, ...   (= A051222)
%C A249306    4,   8,   68,   76,  124,  152, ...   (= A051226)
%C A249306    6, 114,  186,  258,  354,  402, ...   (= A051228)
%C A249306   10,  50,  170,  370,  470,  590, ...   (= A051230)
%C A249306   12,  24, 1308, 1884, 2004, 2364, ...   (= A249134)
%C A249306   etc.
%C A249306 Hence by antidiagonals a permutation of A001477(n).
%C A249306 First column: A248614(n).
%C A249306 a(n) is an alternative sequence for the denominators of the Bernoulli numbers.
%C A249306 First 36 terms of the corresponding clockwise spiral:
%C A249306 .
%C A249306   330------2----138------1---2730------2
%C A249306     |                                  |
%C A249306     |                                  |
%C A249306     1     42------1-----30------2      6
%C A249306     |      |                    |      |
%C A249306     |      |                    |      |
%C A249306   798      2      1------2     66      1
%C A249306     |      |             |      |      |
%C A249306     |      |             |      |      |
%C A249306     2     30------1------6      1    870
%C A249306     |                           |      |
%C A249306     |                           |      |
%C A249306   510------1------6------2---2730      2
%C A249306                                        |
%C A249306                                        |
%C A249306     1------6------2----510------1--14322
%H A249306 <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers</a>
%F A249306 a(2n) = A002445(n), a(2n+1) = A000034(n+1).
%p A249306 Clausen := proc(n) local S, i;
%p A249306 S := numtheory[divisors](n); S := map(i->i+1, S);
%p A249306 S := select(isprime, S); mul(i, i=S) end:
%p A249306 A249306 := n -> `if`(n mod 4 = 3, 1, Clausen(n)):
%p A249306 seq(A249306(n), n=0..59); # _Peter Luschny_, Nov 10 2014
%t A249306 a[n_] := Denominator[BernoulliB[n]]; a[n_ /; Mod[n, 4] == 1] = 2; Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Oct 28 2014 *)
%Y A249306 A variant of the Clausen numbers A141056, A160014. And of A176591.
%Y A249306 Cf. A000034, A002445, A016813, A027642, A051222, A051226, A051228, A051230, A090126, A164020, A248614, A249134.
%K A249306 nonn
%O A249306 0,2
%A A249306 _Paul Curtz_, Oct 28 2014