OFFSET
1,2
LINKS
FORMULA
L.g.f.: -log( Product_{k>=1} (1 - x^prime(k))^k ).
If n = Product (p_j^k_j) then a(n) = Sum (pi(p_j) * p_j), where pi = A000720.
EXAMPLE
a(60) = a(2^2 * 3 * 5) = a(prime(1)^2 * prime(2) * prime(3)) = 1 * 2 + 2 * 3 + 3 * 5 = 23.
MATHEMATICA
nmax = 65; CoefficientList[Series[Sum[k Prime[k] x^Prime[k]/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
a[n_] := Plus @@ (PrimePi[#[[1]]] #[[1]] & /@ FactorInteger[n]); Table[a[n], {n, 1, 65}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 07 2024
STATUS
approved