A320059 Sum of divisors of n^2 that do not divide n.

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.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

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

Cf. A000203, A065764, A072861, A054785.

Sequence in context: A288101 A320913 A329879 * A373002 A270450 A270461

Adjacent sequences: A320056 A320057 A320058 * A320060 A320061 A320062

Keyword

nonn,look

Author

Franklin T. Adams-Watters, Oct 04 2018

Status

approved