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A033196
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a(n) = n^3*Product_{p|n} (1 + 1/p).
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3
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1, 12, 36, 96, 150, 432, 392, 768, 972, 1800, 1452, 3456, 2366, 4704, 5400, 6144, 5202, 11664, 7220, 14400, 14112, 17424, 12696, 27648, 18750, 28392, 26244, 37632, 25230, 64800, 30752, 49152, 52272, 62424, 58800, 93312, 52022, 86640
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OFFSET
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1,2
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LINKS
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FORMULA
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Dirichlet g.f.: zeta(s-2)*zeta(s-3)/zeta(2*s-4).
Multiplicative with a(p^e) = p^e*p^(2*e-1)*(p+1). - Vladeta Jovovic, Nov 16 2001
Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + p/((p+1)*(p^3-1))) = 1.1392293101137663761606045655621290749920977339371831842000361508083066155... - Vaclav Kotesovec, Sep 20 2020
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MATHEMATICA
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a[n_] := n*DivisorSum[n, MoebiusMu[n/#] DivisorSigma[1, #^2]&]; Array[a, 40] (* Jean-François Alcover, Dec 02 2015 *)
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PROG
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(PARI) a(n)=direuler(p=2, n, (1+p^2*X)/(1-p^3*X))[n]
(PARI) a(n)=sumdiv(n, d, moebius(d)*sigma(n^3/d^2)) \\ Benoit Cloitre, Feb 16 2008
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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