

A321562


a(n) = Sum_{d divides n} (1)^(d + n/d) * d^6.


3



1, 65, 730, 4033, 15626, 47450, 117650, 257985, 532171, 1015690, 1771562, 2944090, 4826810, 7647250, 11406980, 16510913, 24137570, 34591115, 47045882, 63019658, 85884500, 115151530, 148035890, 188329050, 244156251, 313742650
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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), 162 (see p. 4 and p. 8).
Index entries for sequences mentioned by Glaisher


FORMULA

G.f.: Sum_{k>=1} (1)^(k+1)*k^6*x^k/(1 + x^k).  Ilya Gutkovskiy, Nov 27 2018


MATHEMATICA

a[n_] := DivisorSum[n, (1)^(# + n/#)*#^6 &]; Array[a, 50] (* Amiram Eldar, Nov 27 2018 *)


PROG

(PARI) apply( A321562(n)=sumdiv(n, d, (1)^(n\dd)*d^6), [1..30]) \\ M. F. Hasler, Nov 26 2018
(MAGMA) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&+[(1)^(k+1)*k^6*x^k/(1 + x^k) : k in [1..2*m]]) )); // G. C. Greubel, Nov 28 2018
(Sage) s=(sum((1)^(k+1)*k^6*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=6 of A322083.
Cf. A321543  A321565, A321807  A321836 for similar sequences.
Sequence in context: A200890 A268265 A088677 * A034680 A017675 A013954
Adjacent sequences: A321559 A321560 A321561 * A321563 A321564 A321565


KEYWORD

sign,mult


AUTHOR

N. J. A. Sloane, Nov 23 2018


STATUS

approved



