A066293 a(n) = A000203(n)^2 - A001157(n) = sigma(n)^2 - sigma_2(n).

0, 4, 6, 28, 10, 94, 14, 140, 78, 194, 22, 574, 26, 326, 316, 620, 34, 1066, 38, 1218, 524, 686, 46, 2750, 310, 914, 780, 2086, 58, 3884, 62, 2604, 1084, 1466, 1004, 6370, 74, 1790, 1436, 5890, 82, 6716, 86, 4494, 3718, 2534, 94, 11966, 798, 5394, 2284

Offset: 1

Author

Labos Elemer, Dec 12 2001

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A001157, A002117, A072861.

Programs

Mathematica

a[n_] := DivisorSigma[1, n]^2 - DivisorSigma[2, n]; Array[a, 50] (* Amiram Eldar, Jul 31 2019 *)

PARI

a(n) = sigma(n)^2 - sigma(n, 2); \\ Michel Marcus, Mar 22 2020

Formula

For p prime, a(p) = 2p.

From Amiram Eldar, Mar 17 2024: (Start)

a(n) = A072861(n) - A001157(n).

Sum_{k=1..n} a(k) ~ c * n^3, where c = zeta(3)/2 = 0.601028451579... . (End)