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

1,1

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

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

Mathematica

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

Prog

(PARI) { for (n=1, 10000, write("b065765.txt", n, " ", sigma(2*n^2)) ) } \\ Harry J. Smith, Oct 30 2009

Crossrefs

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

Sequence in context: A176661 A117561 A353679 * A318738 A146853 A183476

Adjacent sequences: A065762 A065763 A065764 * A065766 A065767 A065768

Keyword

nonn

Author

Labos Elemer, Nov 19 2001

Status

approved