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A352050
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Sum of the 4th powers of the divisor complements of the odd proper divisors of n.
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11
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0, 16, 81, 256, 625, 1312, 2401, 4096, 6642, 10016, 14641, 20992, 28561, 38432, 51331, 65536, 83521, 106288, 130321, 160256, 196963, 234272, 279841, 335872, 391250, 456992, 538083, 614912, 707281, 821312, 923521, 1048576, 1200643, 1336352, 1503651, 1700608, 1874161
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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^4 * Sum_{d|n, d<n, d odd} 1 / d^4.
Sum_{k=1..n} a(k) = c * n^5 / 5, where c = 31*zeta(5)/32 = 1.00452376... . (End)
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EXAMPLE
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a(10) = 10^4 * Sum_{d|10, d<10, d odd} 1 / d^4 = 10^4 * (1/1^4 + 1/5^4) = 10016.
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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)^4, d = select(`<`, numtheory:-divisors(m), n))
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MATHEMATICA
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a[n_] := DivisorSigma[-4, n/2^IntegerExponent[n, 2]] * n^4 - Mod[n, 2]; Array[a, 100] (* Amiram Eldar, Oct 13 2023 *)
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PROG
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(PARI) a(n) = n^4 * sigma(n >> valuation(n, 2), -4) - 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), this sequence (k=4), A352051 (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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