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A185633
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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.
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8
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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(End)
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MAPLE
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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