OFFSET
1,2
COMMENTS
Inverse Möbius transform of n^n * c(n), where c(n) is the characteristic function of primes (A010051). - Wesley Ivan Hurt, Apr 01 2025
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..388
FORMULA
G.f.: Sum_{k>=1} (prime(k) * x)^prime(k)/(1 - x^prime(k)). - Seiichi Manyama, Mar 02 2022
a(n) = Sum_{d|n} d^d * c(d), where c = A010051. - Wesley Ivan Hurt, Apr 01 2025
EXAMPLE
a(6) = 31; a(6) = Sum_{p|6, p prime} p^p = 2^2 + 3^3 = 31.
PROG
(PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, isprime(k)*(k*x)^k/(1-x^k)))) \\ Seiichi Manyama, Mar 02 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Feb 08 2022
STATUS
approved