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

1,5

Comments

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

a(n) has a symmetric representation.

Links

Table of n, a(n) for n=1..60.

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 *)

Prog

(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

Crossrefs

Partial sums of A346879.

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

Sequence in context: A141794 A129227 A252748 * A097161 A274993 A233202

Adjacent sequences: A346866 A346867 A346868 * A346870 A346871 A346872

Keyword

nonn,easy

Author

Omar E. Pol, Aug 18 2021

Status

approved