OFFSET
1,2
COMMENTS
If p is a prime, a(p) = Sum_{d|p} d^tau(p/d) = 1^2 + p^1 = p + 1.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{d|n} (n/d)^tau(d). - Wesley Ivan Hurt, Jun 09 2023
EXAMPLE
a(10) = Sum_{d|10} d^tau(10/d) = 1^4 + 2^2 + 5^2 + 10^1 = 40.
MATHEMATICA
Table[Sum[k^DivisorSigma[0, n/k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 60}]
PROG
(PARI) a(n) = sumdiv(n, d, d^numdiv(n/d)); \\ Michel Marcus, Oct 08 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 12 2021
STATUS
approved