A185633 For odd n, a(n) = 2; for even n, a(n) = denominator of Bernoulli(n)/n; The number 2 alternating with the elements of A006953.

2, 12, 2, 120, 2, 252, 2, 240, 2, 132, 2, 32760, 2, 12, 2, 8160, 2, 14364, 2, 6600, 2, 276, 2, 65520, 2, 12, 2, 3480, 2, 85932, 2, 16320, 2, 12, 2, 69090840, 2, 12, 2, 541200, 2, 75852, 2, 2760, 2, 564, 2, 2227680, 2, 132, 2, 6360

Offset

1,1

Comments

There is an integer sequence b(n) = A053657(n)/2^(n-1) = 1, 1, 6, 6, 360, 360, 45360, 45360, 5443200, 5443200,... which consists of the duplicated entries of A202367.

The ratios of this sequence are b(n+1)/b(n) = 1, 6, 1, 60, 1, 126 .... = a(n)/2, which is a variant of A036283.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A053657(n+1)/A053657(n).

a(2*n) = 2*A036283(n).

From Antti Karttunen, Dec 03 2018: (Start)

a(n) = Product_{d|n} [(1+d)^(1+A286561(n,1+d))]^A010051(1+d) - after Peter J. Cameron's Mar 25 2002 comment in A006863.

A007947(a(n)) = A027760(n)

A001221(a(n)) = A067513(n).

A181819(a(n)) = A322312(n).

(End)

Maple

A185633 := proc(n)
    A053657(n+1)/A053657(n) ;
end proc: # R. J. Mathar, Dec 19 2012

Mathematica

max = 52; s = Expand[Normal[Series[(-Log[1-x]/x)^z, {x, 0, max}]]]; a[n_, k_] := Denominator[Coefficient[s, x^n*z^k]]; A053657 = Prepend[LCM @@@ Table[a[n, k], {n, max}, {k, n}], 1]; a[n_] := A053657[[n+1]]/A053657[[n]]; Table[a[n], {n, 1, max}] (* Jean-François Alcover, Dec 20 2012 *)

Prog

(PARI) A185633(n) = if(n%2, 2, denominator(bernfrac(n)/(n))); \\ Antti Karttunen, Dec 03 2018
(PARI) A185633(n) = { my(m=1); fordiv(n, d, if(isprime(1+d), m *= (1+d)^(1+valuation(n, 1+d)))); (m); }; \\ Antti Karttunen, Dec 03 2018

Crossrefs

Cf. A006953, A007395 (bisections).

Cf. A006863, A027760, A067513, A322312, A322315 (rgs-transform).

Sequence in context: A320975 A222804 A128268 * A246737 A012626 A012629

Adjacent sequences: A185630 A185631 A185632 * A185634 A185635 A185636

Keyword

nonn

Author

Paul Curtz, Dec 18 2012

Extensions

Name edited by Antti Karttunen, Dec 03 2018

Status

approved