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A352051
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Sum of the 5th powers of the divisor complements of the odd proper divisors of n.
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11
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0, 32, 243, 1024, 3125, 7808, 16807, 32768, 59292, 100032, 161051, 249856, 371293, 537856, 762743, 1048576, 1419857, 1897376, 2476099, 3201024, 4101151, 5153664, 6436343, 7995392, 9768750, 11881408, 14408199, 17211392, 20511149, 24407808, 28629151, 33554432, 39296687
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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^5 * Sum_{d|n, d<n, d odd} 1 / d^5.
Sum_{k=1..n} a(k) = c * n^6 / 6, where c = 63*zeta(6)/64 = 1.00144707... . (End)
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EXAMPLE
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a(10) = 10^5 * Sum_{d|10, d<10, d odd} 1 / d^5 = 10^5 * (1/1^5 + 1/5^5) = 100032.
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MAPLE
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f:= proc(n) local m, d;
m:= n/2^padic:-ordp(n, 2);
add((n/d)^5, d = select(`<`, numtheory:-divisors(m), n))
end proc:
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MATHEMATICA
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a[n_] := DivisorSigma[-5, n/2^IntegerExponent[n, 2]] * n^5 - Mod[n, 2]; Array[a, 100] (* Amiram Eldar, Oct 13 2023 *)
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PROG
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(PARI) a(n) = n^5 * sigma(n >> valuation(n, 2), -5) - 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), this sequence (k=5), A352052 (k=6), A352053 (k=7), A352054 (k=8), A352055 (k=9), A352056 (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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