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

Offset: 0

Author

Paul Curtz, Oct 28 2014

Keywords

• nonn

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:

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330------2----138------1---2730------2

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1 42------1-----30------2 6

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798 2 1------2 66 1

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2 30------1------6 1 870

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510------1------6------2---2730 2

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1------6------2----510------1--14322

Links

• Index entries for sequences related to Bernoulli numbers

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.

Programs

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 *)

Formula

a(2n) = A002445(n), a(2n+1) = A000034(n+1).