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%I #52 Apr 25 2022 09:27:30
%S 1,3,5,5,9,9,13,9,11,15,21,15,25,21,21,17,33,21,37,25,29,33,45,27,29,
%T 39,29,35,57,37,61,33,45,51,45,39,73,57,53,45,81,51,85,55,51,69,93,51,
%U 55,55,69,65,105,57,69,63,77,87,117,67,121,93,71,65,81,79,133,85,93,81,141
%N a(n) = n + sopf(n) - omega(n).
%C From _Bernard Schott_, Jun 10 2020: (Start)
%C All terms are odd, but not all odd integers are obtained: see A353046.
%C 1 <= a(n) <= 2n-1 (see formula). (End)
%F a(n) = Sum_{k=1..n} k^(c(k)*(1 - ceiling(n/k) + floor(n/k)), where c is the prime characteristic (A010051).
%F a(n) = n + A055631(n).
%F From _Bernard Schott_, Jun 10 2020: (Start)
%F a(n) = 1 iff n = 1.
%F a(n) = 2*n-1 iff n is prime.
%F a(p^k) = p^k + p - 1 for p prime, k > 0. (End)
%t Table[n - PrimeNu[n] + Sum[p, {p, Select[Divisors[n], PrimeQ]}], {n, 100}]
%o (PARI) a(n) = n + vecsum(factor(n)[, 1]) - omega(n); \\ _Michel Marcus_, Jul 21 2020
%Y Cf. A001221 (omega), A008472 (sopf), A010051, A055631, A353046.
%K nonn,easy
%O 1,2
%A _Wesley Ivan Hurt_, Jun 08 2020
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