A067558 Sum of squares of proper divisors of n.

0, 1, 1, 5, 1, 14, 1, 21, 10, 30, 1, 66, 1, 54, 35, 85, 1, 131, 1, 146, 59, 126, 1, 274, 26, 174, 91, 266, 1, 400, 1, 341, 131, 294, 75, 615, 1, 366, 179, 610, 1, 736, 1, 626, 341, 534, 1, 1106, 50, 755, 299, 866, 1, 1184, 147, 1114, 371, 846, 1, 1860, 1, 966, 581, 1365

Offset: 1

Author

Reinhard Zumkeller, Jan 29 2002

Keywords

• nonn
• easy

Examples

			a(12) = 1^2 + 2^2 + 3^2 + 4^2 + 6^2 = 1 + 4 + 9 + 16 + 36 = 66.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A001157, A002117, A032741.

Programs

Mathematica

Table[DivisorSigma[2, n] - n^2, {n, 1, 64}] (* Jean-François Alcover, Mar 01 2019 *)

PARI

a(n)=sigma(n,2)-n^2 \\ Charles R Greathouse IV, Dec 07 2011

Formula

a(n) = A001157(n) - n^2.

a(n) = 1 if and only if n is prime.

Dirichlet g.f.: zeta(s-2)*(zeta(s) - 1). - Ilya Gutkovskiy, Sep 08 2016

Sum_{k=1..n} a(k) ~ (zeta(3)-1) * n^3 / 3. - Amiram Eldar, Dec 31 2024