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A288420
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a(n) = Sum_{d|n} d^4*A000593(n/d).
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7
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1, 17, 85, 273, 631, 1445, 2409, 4369, 6898, 10727, 14653, 23205, 28575, 40953, 53635, 69905, 83539, 117266, 130341, 172263, 204765, 249101, 279865, 371365, 394406, 485775, 558778, 657657, 707311, 911795, 923553, 1118481, 1245505, 1420163, 1520079, 1883154
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OFFSET
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1,2
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COMMENTS
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Multiplicative because this sequence is the Dirichlet convolution of A000583 and A000593 which are both multiplicative. - Andrew Howroyd, Jul 20 2018
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LINKS
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FORMULA
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Multiplicative with a(2^e) = (16^(e+1)-1)/15 and a(p^e) = (p^(4*e+7) - (p^3+p^2+p+1)*p^(e+1) + p^2 + p + 1)/(p^7 - (p^3+p^2+p+1)*p + p^2 + p + 1) for p > 2.
Sum_{k=1..n} a(k) ~ c * n^5, where c = Pi^4*zeta(5)/480 = (3/16)*zeta(4)*zeta(5) = 0.210429... . (End)
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MATHEMATICA
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f[p_, e_] := (p^(4*e+7) - (p^3+p^2+p+1)*p^(e+1) + p^2 + p + 1)/(p^7 - (p^3+p^2+p+1)*p + p^2 + p + 1); f[2, e_] := (16^(e+1)-1)/15; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Nov 13 2022 *)
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CROSSREFS
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KEYWORD
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mult,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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