OFFSET
1,2
COMMENTS
Sum of aliquot divisors (or aliquot parts) of the n-th positive even number.
a(n) has a symmetric representation.
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
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Aug 20 2021
STATUS
approved