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A285989
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a(0) = 0, a(n) = Sum_{0<d|n, n/d odd} d^4 for n > 0.
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7
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0, 1, 16, 82, 256, 626, 1312, 2402, 4096, 6643, 10016, 14642, 20992, 28562, 38432, 51332, 65536, 83522, 106288, 130322, 160256, 196964, 234272, 279842, 335872, 391251, 456992, 538084, 614912, 707282, 821312, 923522, 1048576, 1200644, 1336352, 1503652, 1700608
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OFFSET
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0,3
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COMMENTS
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Multiplicative because this sequence is the Dirichlet convolution of A000035 and A000583 which are both multiplicative. - Andrew Howroyd, Aug 05 2018
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LINKS
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FORMULA
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Multiplicative with a(2^e) = 2^(4*e) and a(p^e) = (p^(4*e+4)-1)/(p^4-1) for p > 2.
Sum_{k=1..n} a(k) ~ c * n^5, where c = 31*zeta(5)/160 = 0.200904... . (End)
Dirichlet g.f.: zeta(s)*zeta(s-4)*(1-1/2^s). - Amiram Eldar, Jan 08 2023
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MAPLE
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f:= n -> add((n/d)^4, d = numtheory:-divisors(n/2^padic:-ordp(n, 2))); # Robert Israel, Apr 30 2017
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MATHEMATICA
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{0}~Join~Table[DivisorSum[n, Mod[#, 2] (n/#)^4 &], {n, 36}] (* Michael De Vlieger, Aug 05 2018 *)
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PROG
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(PARI) a(n)={sumdiv(n, d, (d%2)*(n/d)^4)} \\ Andrew Howroyd, Aug 05 2018
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CROSSREFS
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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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