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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified August 4 02:24 EDT 2021. Contains 346441 sequences. (Running on oeis4.)