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

Author

Paul Curtz, Dec 18 2012

Keywords

• nonn

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

Crossrefs

Cf. A006953, A007395 (bisections).

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

Programs

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 *)

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

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)

Extensions

Name edited by Antti Karttunen, Dec 03 2018