|
%I #21 Oct 28 2022 07:15:07
%S 3,15,39,63,93,195,171,255,363,465,399,819,549,855,1209,1023,921,1815,
%T 1143,1953,2223,1995,1659,3315,2343,2745,3279,3591,2613,6045,2979,
%U 4095,5187,4605,5301,7623,4221,5715,7137,7905,5169,11115,5679,8379,11253
%N Sum of divisors of twice square numbers.
%C The sum of divisors of 2m^2 [twice a square] always gives remainder r = 3 modulo 6. See A097022.
%H T. D. Noe, <a href="/A065765/b065765.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = sigma(2*n^2) = A000203(2*A000290(n)).
%F a(n) = 3*A065766(n).
%F Sum_{k=1..n} a(k) ~ c * n^3, where c = 12*zeta(3)/Pi^2 = 1.461525... . - _Amiram Eldar_, Oct 28 2022
%t DivisorSigma[1,2*Range[50]^2] (* _Harvey P. Dale_, Sep 06 2015 *)
%o (PARI) { for (n=1, 10000, write("b065765.txt", n, " ", sigma(2*n^2)) ) } \\ _Harry J. Smith_, Oct 30 2009
%Y Cf. A000203, A000290, A002117, A028982, A065766, A097022.
%K nonn
%O 1,1
%A _Labos Elemer_, Nov 19 2001
|
