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