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A321560
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a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^4.
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3
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1, -17, 82, -241, 626, -1394, 2402, -3825, 6643, -10642, 14642, -19762, 28562, -40834, 51332, -61169, 83522, -112931, 130322, -150866, 196964, -248914, 279842, -313650, 391251, -485554, 538084, -578882, 707282, -872644, 923522, -978673, 1200644
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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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G.f.: Sum_{k>=1} (-1)^(k+1)*k^4*x^k/(1 + x^k). - Ilya Gutkovskiy, Nov 27 2018
Multiplicative with a(2^e) = -(7*2^(4*e+1) + 31)/15, and a(p^e) = (p^(4*e+4) - 1)/(p^4 - 1) for p > 2. - Amiram Eldar, Nov 22 2022
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MATHEMATICA
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a[n_] := DivisorSum[n, (-1)^(# + n/#)*#^4 &]; Array[a, 50] (* Amiram Eldar, Nov 27 2018 *)
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PROG
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(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&+[(-1)^(k+1)*k^4*x^k/(1 + x^k) : k in [1..2*m]]) )); // G. C. Greubel, Nov 28 2018
(Sage) s=(sum((-1)^(k+1)*k^4*x^k/(1 + x^k) for k in (1..50))).series(x, 50); a = s.coefficients(x, sparse=False); a[1:] # G. C. Greubel, Nov 28 2018
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CROSSREFS
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KEYWORD
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sign,mult
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AUTHOR
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STATUS
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approved
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