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A067558
Sum of squares of proper divisors of n.
15
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.
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
Sequence in context: A366159 A174504 A270654 * A104792 A120393 A370518
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jan 29 2002
STATUS
approved