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A351273
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Sum of the 10th powers of the squarefree divisors of n.
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11
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1, 1025, 59050, 1025, 9765626, 60526250, 282475250, 1025, 59050, 10009766650, 25937424602, 60526250, 137858491850, 289537131250, 576660215300, 1025, 2015993900450, 60526250, 6131066257802, 10009766650, 16680163512500, 26585860217050, 41426511213650, 60526250
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{d|n} d^10 * mu(d)^2.
Multiplicative with a(p^e) = 1 + p^10. - Amiram Eldar, Feb 06 2022
G.f.: Sum_{k>=1} mu(k)^2 * k^10 * x^k / (1 - x^k). - Ilya Gutkovskiy, Feb 06 2022
Sum_{k=1..n} a(k) ~ c * n^11, where c = zeta(11)/(11*zeta(2)) = 0.0552934... . - Amiram Eldar, Nov 10 2022
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EXAMPLE
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a(4) = 1025; a(4) = Sum_{d|4} d^10 * mu(d)^2 = 1^10*1 + 2^10*1 + 4^10*0 = 1025.
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MATHEMATICA
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a[1] = 1; a[n_] := Times @@ (1 + FactorInteger[n][[;; , 1]]^10); Array[a, 100] (* Amiram Eldar, Feb 06 2022 *)
Table[Total[Select[Divisors[n], SquareFreeQ]^10], {n, 25}] (* Harvey P. Dale, Nov 20 2022 *)
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CROSSREFS
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Sum of the k-th powers of the squarefree divisors of n for k=0..10: A034444 (k=0), A048250 (k=1), A351265 (k=2), A351266 (k=3), A351267 (k=4), A351268 (k=5), A351269 (k=6), A351270 (k=7), A351271 (k=8), A351272 (k=9), this sequence (k=10).
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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