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A370240
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The sum of divisors of n that are cubes of squarefree numbers.
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2
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1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 28, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 28, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 9, 28, 1, 1, 1, 1, 1
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OFFSET
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1,8
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COMMENTS
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LINKS
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FORMULA
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Multiplicative with a(p^e) = 1 for e <= 2, and a(p^e) = 1 + p^3 for e >= 3.
Dirichlet g.f.: zeta(s)*zeta(3*s-3)/zeta(6*s-6).
Sum_{k=1..n} a(k) ~ c * n^(4/3) + n, where c = 3*zeta(4/3)/(2*Pi^2) = 0.5472769126... .
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MATHEMATICA
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f[p_, e_] := If[e <= 2, 1, 1 + p^3]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
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PROG
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(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] <= 2, 1, 1 + f[i, 1]^3)); }
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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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STATUS
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approved
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