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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
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.
Sequence in context: A366427 A366571 A027642 * A347427 A117214 A185972
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.)