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A346878
Sum of the divisors, except for the largest, of the n-th positive even number.
5
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.
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