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

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.

Cf. A000203, A005843, A048050, A062731, A237593, A245092, A244049, A326124, A346870, A346877, A346880, A347153.

Sequence in context: A189211 A301287 A310133 * A034091 A278812 A111717

Adjacent sequences: A346875 A346876 A346877 * A346879 A346880 A346881

Keyword

nonn,easy

Author

Omar E. Pol, Aug 20 2021

Status

approved