OFFSET
1,2
COMMENTS
From Bernard Schott, Jun 10 2020: (Start)
All terms are odd, but not all odd integers are obtained: see A353046.
1 <= a(n) <= 2n-1 (see formula). (End)
FORMULA
a(n) = Sum_{k=1..n} k^(c(k)*(1 - ceiling(n/k) + floor(n/k)), where c is the prime characteristic (A010051).
a(n) = n + A055631(n).
From Bernard Schott, Jun 10 2020: (Start)
a(n) = 1 iff n = 1.
a(n) = 2*n-1 iff n is prime.
a(p^k) = p^k + p - 1 for p prime, k > 0. (End)
MATHEMATICA
Table[n - PrimeNu[n] + Sum[p, {p, Select[Divisors[n], PrimeQ]}], {n, 100}]
PROG
(PARI) a(n) = n + vecsum(factor(n)[, 1]) - omega(n); \\ Michel Marcus, Jul 21 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jun 08 2020
STATUS
approved