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A320059
Sum of divisors of n^2 that do not divide n.
2
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
OFFSET
1,2
COMMENTS
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.
FORMULA
a(n) = sigma(n^2) - sigma(n).
a(n) = A065764(n) - A000203(n).
a(n) = n^2 iff n is prime. - Altug Alkan, Oct 04 2018
MAPLE
map(n -> numtheory:-sigma(n^2)-numtheory:-sigma(n), [$1..100]); # Robert Israel, Oct 04 2018
MATHEMATICA
Table[DivisorSigma[1, n^2] - DivisorSigma[1, n], {n, 70}] (* Vincenzo Librandi, Oct 05 2018 *)
PROG
(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
def A320059(n):
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)
return c1-c2 # Chai Wah Wu, Oct 05 2018
CROSSREFS
KEYWORD
nonn,look
AUTHOR
STATUS
approved