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A067558
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Sum of squares of proper divisors of n.
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14
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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
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1,4
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COMMENTS
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a(n) = A001157(n) - n^2.
a(n) = 1 if and only if n is prime.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
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Dirichlet g.f.: zeta(s-2)*(zeta(s) - 1). - Ilya Gutkovskiy, Sep 08 2016
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EXAMPLE
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a(12) = 1^2 + 2^2 + 3^2 + 4^2 + 6^2 = 1 + 4 + 9 + 16 + 36 = 66.
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MATHEMATICA
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Table[DivisorSigma[2, n] - n^2, {n, 1, 64}] (* Jean-François Alcover, Mar 01 2019 *)
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PROG
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(PARI) a(n)=sigma(n, 2)-n^2 \\ Charles R Greathouse IV, Dec 07 2011
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CROSSREFS
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Cf. A001157, A032741.
Sequence in context: A300291 A174504 A270654 * A104792 A120393 A094368
Adjacent sequences: A067555 A067556 A067557 * A067559 A067560 A067561
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Jan 29 2002
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STATUS
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approved
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