A321819 a(n) = Sum_{d|n, n/d odd} d^10 for n > 0.

1, 1024, 59050, 1048576, 9765626, 60467200, 282475250, 1073741824, 3486843451, 10000001024, 25937424602, 61918412800, 137858491850, 289254656000, 576660215300, 1099511627776, 2015993900450, 3570527693824, 6131066257802, 10240001048576

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^(2*k)). - Ilya Gutkovskiy, Dec 22 2018

From Amiram Eldar, Nov 02 2022: (Start)

Multiplicative with a(2^e) = 2^(10*e) and a(p^e) = (p^(10*e+10)-1)/(p^10-1) for p > 2.

Sum_{k=1..n} a(k) ~ c * n^11, where c = 2047*zeta(11)/22528 = 0.090909606... . (End)

Dirichlet g.f.: zeta(s)*zeta(s-10)*(1-1/2^s). - Amiram Eldar, Jan 09 2023

Mathematica

a[n_] := DivisorSum[n, #^10 &, OddQ[n/#] &]; Array[a, 30] (* Amiram Eldar, Nov 26 2018 *)

Prog

(PARI) apply( A321819(n)=sumdiv(n, d, if(bittest(n\d, 0), d^10)), [1..30]) \\ M. F. Hasler, Nov 26 2018

Crossrefs

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

Cf. A013669.

Sequence in context: A351608 A030629 A056587 * A231309 A134847 A066371

Adjacent sequences: A321816 A321817 A321818 * A321820 A321821 A321822

Keyword

nonn,mult

Author

N. J. A. Sloane, Nov 24 2018

Status

approved