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A077454
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a(n) = sigma_3(n^3)/sigma(n^3).
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4
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1, 39, 511, 2359, 12621, 19929, 101179, 149943, 368089, 492219, 1611831, 1205449, 4457701, 3945981, 6449331, 9588151, 22722609, 14355471, 44576623, 29772939, 51702469, 62861409, 141611691, 76620873, 196890121, 173850339, 268218727, 238681261, 574336533, 251523909
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history;
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OFFSET
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1,2
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A001158(n^3)/A000203(n^3).
Multiplicative with a(p^e) = (p^(6*e+2) + p^(3*e+1) + 1)/(p^2 + p + 1). - Amiram Eldar, Sep 09 2020
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EXAMPLE
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a(2) = sigma_3(2^3)/sigma(2^3) = 585/15 = 39.
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MATHEMATICA
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f[p_, e_] := (p^(6*e+2) + p^(3*e+1) + 1)/(p^2 + p + 1); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 30] (* Amiram Eldar, Sep 09 2020 *)
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PROG
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(PARI) a(n)=sumdiv(n^3, d, d^3)/sigma(n^3)
(PARI) a(n) = my(f=factor(n^3)); sigma(f, 3)/sigma(f); \\ Michel Marcus, Sep 09 2020
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CROSSREFS
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Cf. A000203, A000578, A001158, A057660, A077455, A077456.
Sequence in context: A229517 A254871 A193072 * A142976 A200409 A341565
Adjacent sequences: A077451 A077452 A077453 * A077455 A077456 A077457
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KEYWORD
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nonn,easy,mult
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AUTHOR
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Benoit Cloitre, Nov 30 2002
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STATUS
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approved
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