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A347153 Sum of all divisors, except the largest of every number, of the first n odd numbers. 3
0, 1, 2, 3, 7, 8, 9, 18, 19, 20, 31, 32, 38, 51, 52, 53, 68, 81, 82, 99, 100, 101, 134, 135, 143, 164, 165, 182, 205, 206, 207, 248, 267, 268, 295, 296, 297, 346, 365, 366, 406, 407, 430, 463, 464, 485, 520, 545, 546, 603, 604, 605, 692, 693, 694, 735, 736, 765, 830, 855 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Sum of all aliquot divisors (or aliquot parts) of the first n odd numbers.

Partial sums of the odd-indexed terms of A001065.

a(n) has a symmetric representation.

LINKS

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

FORMULA

a(n) = A001477(n-1) + A346869(n).

G.f.: (1/(1 - x)) * Sum_{k>=0} (2*k + 1) * x^(3*k + 2) / (1 - x^(2*k + 1)). - Ilya Gutkovskiy, Aug 20 2021

MATHEMATICA

s[n_] := DivisorSigma[1, 2*n - 1] - 2*n + 1; Accumulate @ Array[s, 100] (* Amiram Eldar, Aug 20 2021 *)

PROG

(Python)

from sympy import divisors

from itertools import accumulate

def A346877(n): return sum(divisors(2*n-1)[:-1])

def aupton(nn): return list(accumulate(A346877(n) for n in range(1, nn+1)))

print(aupton(60)) # Michael S. Branicky, Aug 20 2021

(PARI) a(n) = sum(k=1, n, k = 2*k-1; sigma(k)-k); \\ Michel Marcus, Aug 20 2021

CROSSREFS

Partial sums of A346877.

Cf. A000203, A001065, A001477, A005408, A008438, A048050, A153485, A237593, A245092, A244049, A326123, A346869, A346878, A346879, A347154.

Sequence in context: A123644 A246440 A332699 * A105266 A246448 A054996

Adjacent sequences:  A347150 A347151 A347152 * A347154 A347155 A347156

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Aug 20 2021

STATUS

approved

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Last modified October 21 15:17 EDT 2021. Contains 348155 sequences. (Running on oeis4.)