A346878 - OEIS

A346878

Sum of the divisors, except for the largest, of the n-th positive even number.

1, 3, 6, 7, 8, 16, 10, 15, 21, 22, 14, 36, 16, 28, 42, 31, 20, 55, 22, 50, 54, 40, 26, 76, 43, 46, 66, 64, 32, 108, 34, 63, 78, 58, 74, 123, 40, 64, 90, 106, 44, 140, 46, 92, 144, 76, 50, 156, 73, 117, 114, 106, 56, 172, 106, 136, 126, 94, 62, 240, 64, 100, 186, 127

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OFFSET

1,2

COMMENTS

Sum of aliquot divisors (or aliquot parts) of the n-th positive even number.

a(n) has a symmetric representation.

LINKS

Table of n, a(n) for n=1..64.

FORMULA

a(n) = A001065(2*n).

a(n) = 1 + A346880(n).

Sum_{k=1..n} a(k) = (5*Pi^2/24 - 1) * n^2 + O(n*log(n)). - Amiram Eldar, Mar 17 2024

EXAMPLE

For n = 5 the 5th even number is 10 and the divisors of 10 are [1, 2, 5, 10] and the sum of the divisors of 10 except for the largest is 1 + 2 + 5 = 8, so a(5) = 8.

MATHEMATICA

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

PROG

(Python)

from sympy import divisors

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

print([a(n) for n in range(1, 65)]) # Michael S. Branicky, Aug 20 2021

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

CROSSREFS

Bisection of A001065.

Partial sums give A347154.