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A351313
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Sum of the 7th powers of the square divisors of n.
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11
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1, 1, 1, 16385, 1, 1, 1, 16385, 4782970, 1, 1, 16385, 1, 1, 1, 268451841, 1, 4782970, 1, 16385, 1, 1, 1, 16385, 6103515626, 1, 4782970, 16385, 1, 1, 1, 268451841, 1, 1, 1, 78368963450, 1, 1, 1, 16385, 1, 1, 1, 16385, 4782970, 1, 1, 268451841, 678223072850, 6103515626, 1
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = Sum_{d^2|n} (d^2)^7.
Multiplicative with a(p) = (p^(14*(1+floor(e/2))) - 1)/(p^14 - 1). - Amiram Eldar, Feb 07 2022
Dirichlet g.f.: zeta(s) * zeta(2*s-14).
Sum_{k=1..n} a(k) ~ (zeta(15/2)/15) * n^(15/2). (End)
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EXAMPLE
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a(16) = 268451841; a(16) = Sum_{d^2|16} (d^2)^7 = (1^2)^7 + (2^2)^7 + (4^2)^7 = 268451841.
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MATHEMATICA
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f[p_, e_] := (p^(14*(1 + Floor[e/2])) - 1)/(p^14 - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Feb 07 2022 *)
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CROSSREFS
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Sum of the k-th powers of the square divisors of n for k=0..10: A046951 (k=0), A035316 (k=1), A351307 (k=2), A351308 (k=3), A351309 (k=4), A351310 (k=5), A351311 (k=6), this sequence (k=7), A351314 (k=8), A351315 (k=9), A351315 (k=10).
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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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