A053807 a(n) = Sum_{k=1..n, n mod k = 1} k^2.

0, 0, 4, 9, 20, 25, 49, 49, 84, 90, 129, 121, 209, 169, 249, 259, 340, 289, 454, 361, 545, 499, 609, 529, 849, 650, 849, 819, 1049, 841, 1299, 961, 1364, 1219, 1449, 1299, 1910, 1369, 1809, 1699, 2209, 1681, 2499, 1849, 2561, 2365, 2649

Offset: 1

Author

N. J. A. Sloane, Apr 07 2000

Keywords

• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001157.

Programs

Magma

[0] cat [DivisorSigma(2, n-1) -1: n in [2..50]]; // G. C. Greubel, Feb 28 2019

Maple

f:= n -> numtheory:-sigma[2](n-1) - 1: f(1):= 0:
map(f, [$1..100]); # Robert Israel, Jan 29 2018

Mathematica

a[1] = 0; a[n_] := DivisorSigma[2, n - 1] - 1;
Array[a, 50] (* Jean-François Alcover, Feb 28 2019 *)

PARI

concat([0], vector(50, n, n++; sigma(n-1, 2) -1)) \\ G. C. Greubel, Feb 28 2019

Sage

[0] + [sigma(n-1, 2) - 1 for n in (2..50)] # G. C. Greubel, Feb 28 2019

Formula

a(n) = sigma_2(n-1) - 1 for n >= 2.

G.f.: -x^2/(1 - x) + Sum_{k>=1} k^2*x^(k+1)/(1 - x^k). - Ilya Gutkovskiy, Mar 17 2017