A346880 Sum of the divisors, except the smallest and the largest, of the n-th positive even number.

0, 2, 5, 6, 7, 15, 9, 14, 20, 21, 13, 35, 15, 27, 41, 30, 19, 54, 21, 49, 53, 39, 25, 75, 42, 45, 65, 63, 31, 107, 33, 62, 77, 57, 73, 122, 39, 63, 89, 105, 43, 139, 45, 91, 143, 75, 49, 155, 72, 116, 113, 105, 55, 171, 105, 135, 125, 93, 61, 239, 63, 99, 185, 126, 121

Offset

1,2

Comments

a(n) has a symmetric representation.

Links

Table of n, a(n) for n=1..65.

Formula

a(n) = A048050(2*n).

Sum_{k=1..n} a(k) = (5*Pi^2/24 - 1) * n^2 + O(n*log(n)). - Amiram Eldar, Mar 21 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 the smaller and the largest is 2 + 5 = 7, so a(5) = 7.

Mathematica

a[n_] := DivisorSigma[1, 2*n] - 2*n - 1; Array[a, 100] (* Amiram Eldar, Aug 19 2021 *)

Prog

(Python)
from sympy import divisors
def a(n): return sum(divisors(2*n)[1:-1])
print([a(n) for n in range(1, 66)]) # Michael S. Branicky, Aug 19 2021

Crossrefs

Bisection of A048050.

Partial sums give A346870.

Cf. A000203, A005843, A062731, A237593, A245092, A244049, A326124, A346879.

Sequence in context: A244314 A014489 A286270 * A344865 A350130 A033959

Adjacent sequences: A346877 A346878 A346879 * A346881 A346882 A346883

Keyword

nonn,easy

Author

Omar E. Pol, Aug 18 2021

Status

approved