A321555 a(n) = Sum_{d|n} (-1)^(n/d+1)*d^10.

1, 1023, 59050, 1047551, 9765626, 60408150, 282475250, 1072692223, 3486843451, 9990235398, 25937424602, 61857886550, 137858491850, 288972180750, 576660215300, 1098436836351, 2015993900450, 3567040850373, 6131066257802, 10229991281926, 16680163512500, 26533985367846, 41426511213650, 63342475768150

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

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} k^10*x^k/(1 + x^k). - Seiichi Manyama, Nov 25 2018

From Amiram Eldar, Nov 11 2022: (Start)

Multiplicative with a(2^e) = (511*2^(10*e+1)+1)/1023, and a(p^e) = (p^(10*e+10) - 1)/(p^10 - 1) if p > 2.

Sum_{k=1..n} a(k) ~ c * n^11, where c = 93*zeta(11)/1024 = 0.0908651... . (End)

Mathematica

f[p_, e_] := (p^(10*e + 10) - 1)/(p^10 - 1); f[2, e_] := (511*2^(10*e + 1) + 1)/1023; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Nov 11 2022 *)

Prog

(PARI) apply( A321555(n)=sumdiv(n, d, (-1)^(n\d-1)*d^10), [1..30]) \\ M. F. Hasler, Nov 26 2018

Crossrefs

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

Cf. A013669.

Sequence in context: A069095 A024008 A123867 * A321549 A160959 A022192

Adjacent sequences: A321552 A321553 A321554 * A321556 A321557 A321558

Keyword

nonn,mult

Author

N. J. A. Sloane, Nov 23 2018

Status

approved