A175361 Partial sums of A000141.

1, 13, 73, 233, 485, 797, 1341, 2301, 3321, 4197, 5757, 8157, 10237, 12277, 15541, 19701, 23793, 27273, 31653, 38853, 45405, 50013, 58173, 68733, 76957, 84769, 94969, 108089, 120569, 130673, 144817, 164017, 180397, 191917, 209317, 234277, 252673, 269113, 293593

Offset: 0

Author

R. J. Mathar, Apr 24 2010

Keywords

• nonn

Comments

The 6th row of A122510.

Crossrefs

Cf. A000141, A055412, A122510.

Programs

Mathematica

CoefficientList[Series[EllipticTheta[3,x]^6/(1-x),{x,0,35}],x] (* Stefano Spezia, Jun 21 2024 *)

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

Formula

a(n^2) = A055412(n).

G.f.: theta_3(x)^6 / (1 - x). - Ilya Gutkovskiy, Feb 13 2021