A321817 a(n) = Sum_{d|n, n/d odd} d^6 for n > 0.

1, 64, 730, 4096, 15626, 46720, 117650, 262144, 532171, 1000064, 1771562, 2990080, 4826810, 7529600, 11406980, 16777216, 24137570, 34058944, 47045882, 64004096, 85884500, 113379968, 148035890, 191365120, 244156251, 308915840, 387952660

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^6*x^k/(1 - x^(2*k)). - Ilya Gutkovskiy, Dec 22 2018

From Amiram Eldar, Nov 02 2022: (Start)

Multiplicative with a(2^e) = 2^(6*e) and a(p^e) = (p^(6*e+6)-1)/(p^6-1) for p > 2.

Sum_{k=1..n} a(k) ~ c * n^7, where c = 127*zeta(7)/896 = 0.142924... . (End)

Dirichlet g.f.: zeta(s)*zeta(s-6)*(1-1/2^s). - Amiram Eldar, Jan 08 2023

Mathematica

a[n_] := DivisorSum[n, #^6 &, OddQ[n/#] &]; Array[a, 30] (* Amiram Eldar, Nov 02 2022 *)

Prog

(PARI) apply( A321817(n)=sumdiv(n, d, if(bittest(n\d, 0), d^6)), [1..30]) \\ M. F. Hasler, Nov 26 2018

Crossrefs

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

Cf. A013665.

Sequence in context: A092758 A030516 A056573 * A231305 A357391 A108538

Adjacent sequences: A321814 A321815 A321816 * A321818 A321819 A321820

Keyword

nonn,mult

Author

N. J. A. Sloane, Nov 24 2018

Status

approved