A346869 Sum of all divisors, except the smallest and the largest of every number, of the first n odd numbers.

0, 0, 0, 0, 3, 3, 3, 11, 11, 11, 21, 21, 26, 38, 38, 38, 52, 64, 64, 80, 80, 80, 112, 112, 119, 139, 139, 155, 177, 177, 177, 217, 235, 235, 261, 261, 261, 309, 327, 327, 366, 366, 388, 420, 420, 440, 474, 498, 498, 554, 554, 554, 640, 640, 640, 680, 680, 708, 772, 796

Offset: 1

Author

Omar E. Pol, Aug 18 2021

Keywords

• nonn
• easy

Comments

Partial sums of the odd-indexed terms of Chowla's function A048050.

a(n) has a symmetric representation.

Crossrefs

Partial sums of A346879.

Cf. A000203, A005408, A008438, A048050, A237593, A245092, A244049, A326123, A346870.

Programs

Maple

a:= proc(n) option remember; `if`(n=1, 0,
      a(n-1)+numtheory[sigma](2*n-1)-2*n)
    end:
seq(a(n), n=1..60);  # Alois P. Heinz, Aug 19 2021

Mathematica

s[1] = 0; s[n_] := DivisorSigma[1, 2*n - 1] - 2*n; Accumulate @ Array[s, 50] (* Amiram Eldar, Aug 19 2021 *)
Accumulate[Join[{0},Table[DivisorSigma[1,n]-n-1,{n,3,151,2}]]] (* Harvey P. Dale, Jul 29 2023 *)

Python

from sympy import divisors
from itertools import accumulate
def A346879(n): return sum(divisors(2*n-1)[1:-1])
def aupton(nn): return list(accumulate(A346879(n) for n in range(1, nn+1)))
print(aupton(60)) # Michael S. Branicky, Aug 19 2021