A103636 a(n) = Sum_{d|n, d==0 mod 3} d^2.

0, 0, 9, 0, 0, 45, 0, 0, 90, 0, 0, 189, 0, 0, 234, 0, 0, 450, 0, 0, 450, 0, 0, 765, 0, 0, 819, 0, 0, 1170, 0, 0, 1098, 0, 0, 1890, 0, 0, 1530, 0, 0, 2250, 0, 0, 2340, 0, 0, 3069, 0, 0, 2610, 0, 0, 4095, 0, 0, 3258, 0, 0, 4914, 0, 0, 4500, 0, 0, 5490, 0, 0, 4770, 0, 0, 7650

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..9999

Formula

a(3*k) = 9*A001157(k), a(3*k+1) = a(3*k+2) = 0. - Robert Israel, Jan 11 2018

Sum_{k=1..n} a(k) ~ zeta(3) * n^3 / 9. - Amiram Eldar, Aug 30 2024

Maple

seq(op([0, 0, 9*numtheory:-sigma[2](k)]), k=1..50); # Robert Israel, Jan 11 2018

Mathematica

Table[Total[Select[Divisors[n], Divisible[#, 3]&]^2], {n, 100}] (* Harvey P. Dale, May 07 2014 *)
a[n_] := If[Divisible[n, 3], 9 * DivisorSigma[2, n/3], 0]; Array[a, 100] (* Amiram Eldar, Aug 30 2024 *)

Prog

(PARI) a(n) = if(n % 3, 0, 9 * sigma(n/3, 2)); \\ Amiram Eldar, Aug 30 2024

Crossrefs

Cf. A001157, A002117.

Sequence in context: A341808 A340946 A255292 * A278006 A221804 A275107

Adjacent sequences: A103633 A103634 A103635 * A103637 A103638 A103639

Keyword

nonn,easy

Author

Ralf Stephan, Feb 11 2005

Status

approved