OFFSET
1,1
FORMULA
G.f.: (1/(1 - x)) * (2*x/(1 - x) + Sum_{k>=2} (prime(k) - prime(k-1))*x^k/(1 - x^k)).
Sum_{k=1..n} mu(k) * a(floor(n/k)) = prime(n).
MATHEMATICA
Table[Sum[Prime[Floor[n/k]], {k, 1, n}], {n, 1, 60}]
g[1] = 2; g[n_] := Prime[n] - Prime[n - 1]; a[n_] := Sum[Sum[g[d], {d, Divisors[k]}], {k, 1, n}]; Table[a[n], {n, 1, 60}]
PROG
(PARI) a(n) = sum(k=1, n, prime(n\k)); \\ Michel Marcus, Mar 22 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 21 2020
STATUS
approved