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A366146
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The sum of divisors of the largest divisor of n that is a cubefull number (A036966).
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3
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1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 31, 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 40, 1, 1, 1, 1, 63, 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 31, 1, 1, 1, 1, 1, 40, 1, 15, 1, 1, 1, 1, 1, 1, 1, 127, 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 31, 121, 1
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OFFSET
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1,8
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LINKS
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FORMULA
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a(n) >= 1, with equality if and only if n is cubefree (A004709).
a(n) <= A000203(n), with equality if and only if n is cubefull (A036966).
Multiplicative with a(p^e) = 1 if e <= 2 and (p^(e+1)-1)/(p-1) otherwise.
Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 - 1/p^(s-1) + 1/p^(3*s-3) + 1/p^(3*s-2) + 1/p^(3*s-1) - 1/p^(4*s-3) - 1/p^(4*s-2)).
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MATHEMATICA
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f[p_, e_] := If[e < 3, 1, (p^(e+1)-1)/(p-1)]; 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), p = f[, 1], e = f[, 2]); prod(i = 1, #p, if(e[i] < 3, 1, (p[i]^(e[i]+1)-1)/(p[i]-1)))};
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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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