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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 is 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-Fran├žois 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: A132181 A291646 A027642 * A117214 A185972 A182918

Adjacent sequences:  A249303 A249304 A249305 * A249307 A249308 A249309

KEYWORD

nonn

AUTHOR

Paul Curtz, Oct 28 2014

STATUS

approved

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Last modified February 25 00:39 EST 2018. Contains 299630 sequences. (Running on oeis4.)