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A352056
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Sum of the 10th powers of the divisor complements of the odd proper divisors of n.
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11
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0, 1024, 59049, 1048576, 9765625, 60467200, 282475249, 1073741824, 3486843450, 10000001024, 25937424601, 61918412800, 137858491849, 289254656000, 576660215299, 1099511627776, 2015993900449, 3570527693824, 6131066257801, 10240001048576, 16680163512499
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = n^10 * Sum_{d|n, d<n, d odd} 1 / d^10.
G.f.: Sum_{k>=2} k^10 * x^k / (1 - x^(2*k)). - Ilya Gutkovskiy, May 19 2023
Sum_{k=1..n} a(k) = c * n^11 / 11, where c = 2047*zeta(11)/2048 = 1.00000566605... . (End)
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EXAMPLE
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a(10) = 10^10 * Sum_{d|10, d<10, d odd} 1 / d^10 = 10^10 * (1/1^10 + 1/5^10) = 10000001024.
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MATHEMATICA
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a[n_] := DivisorSigma[-10, n/2^IntegerExponent[n, 2]] * n^10 - Mod[n, 2]; Array[a, 100] (* Amiram Eldar, Oct 13 2023 *)
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PROG
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(PARI) a(n) = n^10 * sigma(n >> valuation(n, 2), -10) - n % 2; \\ Amiram Eldar, Oct 13 2023
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CROSSREFS
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Sum of the k-th powers of the divisor complements of the odd proper divisors of n for k=0..10: A091954 (k=0), A352047 (k=1), A352048 (k=2), A352049 (k=3), A352050 (k=4), A352051 (k=5), A352052 (k=6), A352053 (k=7), A352054 (k=8), A352055 (k=9), this sequence (k=10).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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