A067558 - OEIS

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

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OFFSET

1,4

LINKS

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

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

EXAMPLE

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