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

1,4

Comments

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

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001157, A032741.

Sequence in context: A366159 A174504 A270654 * A104792 A120393 A370518

Adjacent sequences: A067555 A067556 A067557 * A067559 A067560 A067561

Keyword

nonn

Author

Reinhard Zumkeller, Jan 29 2002

Status

approved