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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.

%I A185633 #29 Dec 03 2018 18:29:03
%S A185633 2,12,2,120,2,252,2,240,2,132,2,32760,2,12,2,8160,2,14364,2,6600,2,
%T A185633 276,2,65520,2,12,2,3480,2,85932,2,16320,2,12,2,69090840,2,12,2,
%U A185633 541200,2,75852,2,2760,2,564,2,2227680,2,132,2,6360
%N 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.
%C A185633 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.
%C A185633 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.
%H A185633 Antti Karttunen, <a href="/A185633/b185633.txt">Table of n, a(n) for n = 1..16384</a>
%F A185633 a(n) = A053657(n+1)/A053657(n).
%F A185633 a(2*n) = 2*A036283(n).
%F A185633 From _Antti Karttunen_, Dec 03 2018: (Start)
%F A185633 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.
%F A185633 A007947(a(n)) = A027760(n)
%F A185633 A001221(a(n)) = A067513(n).
%F A185633 A181819(a(n)) = A322312(n).
%F A185633 (End)
%p A185633 A185633 := proc(n)
%p A185633     A053657(n+1)/A053657(n) ;
%p A185633 end proc: # _R. J. Mathar_, Dec 19 2012
%t A185633 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 *)
%o A185633 (PARI) A185633(n) = if(n%2,2,denominator(bernfrac(n)/(n))); \\ _Antti Karttunen_, Dec 03 2018
%o A185633 (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
%Y A185633 Cf. A006953, A007395 (bisections).
%Y A185633 Cf. A006863, A027760, A067513, A322312, A322315 (rgs-transform).
%K A185633 nonn
%O A185633 1,1
%A A185633 _Paul Curtz_, Dec 18 2012
%E A185633 Name edited by _Antti Karttunen_, Dec 03 2018