A065765 Sum of divisors of twice square numbers.

3, 15, 39, 63, 93, 195, 171, 255, 363, 465, 399, 819, 549, 855, 1209, 1023, 921, 1815, 1143, 1953, 2223, 1995, 1659, 3315, 2343, 2745, 3279, 3591, 2613, 6045, 2979, 4095, 5187, 4605, 5301, 7623, 4221, 5715, 7137, 7905, 5169, 11115, 5679, 8379, 11253

Offset: 1

Author

Labos Elemer, Nov 19 2001

Keywords

• nonn

Comments

The sum of divisors of 2m^2 [twice a square] always gives remainder r = 3 modulo 6. See A097022.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A000290, A002117, A028982, A065766, A097022.

Programs

Mathematica

DivisorSigma[1,2*Range[50]^2] (* Harvey P. Dale, Sep 06 2015 *)

PARI

a(n) = { sigma(2*n^2) } \\ Harry J. Smith, Oct 30 2009

Formula

a(n) = sigma(2*n^2) = A000203(2*A000290(n)).

a(n) = 3*A065766(n).

Sum_{k=1..n} a(k) ~ c * n^3, where c = 12*zeta(3)/Pi^2 = 1.461525... . - Amiram Eldar, Oct 28 2022