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

0,2

Comments

The 6th row of A122510.

Links

Table of n, a(n) for n=0..38.

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

Cf. A000141, A055412, A122510.

Sequence in context: A139873 A142787 A084218 * A125258 A060886 A081586

Adjacent sequences: A175358 A175359 A175360 * A175362 A175363 A175364

Keyword

nonn

Author

R. J. Mathar, Apr 24 2010

Status

approved