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A320059
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Sum of divisors of n^2 that do not divide n.
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2
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0, 4, 9, 24, 25, 79, 49, 112, 108, 199, 121, 375, 169, 375, 379, 480, 289, 808, 361, 919, 709, 895, 529, 1591, 750, 1239, 1053, 1711, 841, 2749, 961, 1984, 1681, 2095, 1719, 3660, 1369, 2607, 2323, 3847, 1681, 5091, 1849, 4039, 3673, 3799, 2209, 6519, 2744, 5374
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OFFSET
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1,2
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COMMENTS
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sigma(n^2) is always odd, so this sequence has the opposite parity from sigma(n): even if n is a square or twice a square, odd otherwise.
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LINKS
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FORMULA
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a(n) = sigma(n^2) - sigma(n).
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MAPLE
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map(n -> numtheory:-sigma(n^2)-numtheory:-sigma(n), [$1..100]); # Robert Israel, Oct 04 2018
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MATHEMATICA
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Table[DivisorSigma[1, n^2] - DivisorSigma[1, n], {n, 70}] (* Vincenzo Librandi, Oct 05 2018 *)
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PROG
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(PARI) a(n) = sigma(n^2)-sigma(n)
(Magma) [DivisorSigma(1, n^2) - DivisorSigma(1, n): n in [1..70]]; // Vincenzo Librandi, Oct 05 2018
(Python)
from __future__ import division
from sympy import factorint
c1, c2 = 1, 1
for p, a in factorint(n).items():
c1 *= (p**(2*a+1)-1)//(p-1)
c2 *= (p**(a+1)-1)//(p-1)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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