OFFSET
1,4
FORMULA
a(p^k) = p^pi(p^(k-1)), for p prime and k >= 1. - Wesley Ivan Hurt, Jun 26 2024
EXAMPLE
a(12) = Sum_{p|12} p^pi(12/p) = 2^pi(6) + 3^pi(4) = 2^3 + 3^2 = 17.
MATHEMATICA
Table[Sum[k^PrimePi[n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]
PROG
(Python)
from sympy import primefactors, primepi
def A345301(n): return sum(p**primepi(n//p) for p in primefactors(n)) # Chai Wah Wu, Jun 13 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 13 2021
STATUS
approved