OFFSET
0,2
COMMENTS
The 6th row of A122510.
FORMULA
a(n^2) = A055412(n).
G.f.: theta_3(x)^6 / (1 - x). - Ilya Gutkovskiy, Feb 13 2021
MATHEMATICA
CoefficientList[Series[EllipticTheta[3, x]^6/(1-x), {x, 0, 35}], x] (* Stefano Spezia, Jun 21 2024 *)
PROG
(Python)
from math import prod
from sympy import factorint
def A175361(n):
c = 1
for m in range(1, n+1):
f = [(p, e, (0, 1, 0, -1)[p&3]) for p, e in factorint(m).items()]
c += (prod((p**(e+1<<1)-a)//(p**2-a) for p, e, a in f)<<2)-prod(((k:=p**2*a)**(e+1)-1)//(k-1) for p, e, a in f)<<2
return c # Chai Wah Wu, Jun 21 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Apr 24 2010
STATUS
approved