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A321560 a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^4. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

J. W. L. Glaisher, On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares, Quart. J. Math. 38 (1907), 1-62 (see p. 4 and p. 8).

Index entries for sequences mentioned by Glaisher

FORMULA

G.f.: Sum_{k>=1} (-1)^(k+1)*k^4*x^k/(1 + x^k). - Ilya Gutkovskiy, Nov 27 2018

MATHEMATICA

a[n_] := DivisorSum[n, (-1)^(# + n/#)*#^4 &]; Array[a, 50] (* Amiram Eldar, Nov 27 2018 *)

PROG

(PARI) apply( A321560(n)=sumdiv(n, d, (-1)^(n\d-d)*d^4), [1..30]) \\ M. F. Hasler, Nov 26 2018

(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

CROSSREFS

Column k=4 of A322083.

Cf. A321543 - A321565, A321807 - A321836 for similar sequences.

Sequence in context: A053826 A184982 A088687 * A034678 A065960 A017671

Adjacent sequences:  A321557 A321558 A321559 * A321561 A321562 A321563

KEYWORD

sign,mult

AUTHOR

N. J. A. Sloane, Nov 23 2018

STATUS

approved

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Last modified December 12 22:06 EST 2019. Contains 329963 sequences. (Running on oeis4.)