OFFSET
1,2
COMMENTS
Inverse Möbius transform of prime(n) * c(n), where c(n) is the characteristic function of primes (A010051). - Wesley Ivan Hurt, Jun 29 2024
FORMULA
From Wesley Ivan Hurt, Jun 29 2024: (Start)
a(n) = Sum_{d|n} prime(d) * c(d), where c = A010051.
a(p^k) = prime(p), for prime p and k >= 1. (End)
EXAMPLE
a(6) = 8; a(6) = Sum_{p|6, p prime} prime(p) = prime(2) + prime(3) = 3 + 5 = 8.
MATHEMATICA
Table[DivisorSum[n, Prime[#] &, PrimeQ[#] &], {n, 100}] (* Wesley Ivan Hurt, Jun 29 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Feb 08 2022
STATUS
approved