OFFSET
1,2
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
FORMULA
Multiplicative with a(2^e) = (4^(e+1)-1)/3 and a(p^e) = (p^(2*e+1)-1)/(p-1) for an odd prime p. - Vladeta Jovovic, Dec 01 2001
Sum_{k=1..n} a(k) ~ c * n^3, where c = 4*zeta(3)/Pi^2 = 0.487175... . - Amiram Eldar, Oct 28 2022
Dirichlet g.f.: zeta(s)*zeta(s-1)*zeta(s-2)/(zeta(2*s-2)*(1+2/2^s)). - Amiram Eldar, Feb 12 2023
MAPLE
with(numtheory): [sigma(2*n^2)/3$n=1..50]; # Muniru A Asiru, Dec 07 2018
MATHEMATICA
Array[DivisorSigma[1, 2 #^2]/3 &, 49] (* Michael De Vlieger, Dec 06 2018 *)
PROG
(PARI) { for (n=1, 1000, write("b065766.txt", n, " ", sigma(2*n^2)/3) ) } \\ Harry J. Smith, Oct 30 2009
(Magma) [SumOfDivisors(2*n^2)/3: n in [1..60]]; // Vincenzo Librandi, Dec 07 2018
(GAP) List([1..50], n->Sigma(2*n^2))/3; # Muniru A Asiru, Dec 07 2018
(Python)
from sympy import divisor_sigma
for n in range(1, 50): print(divisor_sigma(2*n**2, 1)/3) # Stefano Spezia, Dec 07 2018
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Labos Elemer, Nov 19 2001
STATUS
approved