A333449 - OEIS

A333449

a(n) = Sum_{k=1..n} prime(floor(n/k)).

2, 5, 9, 14, 20, 27, 33, 40, 48, 61, 65, 80, 86, 95, 107, 120, 128, 141, 149, 168, 178, 189, 195, 218, 232, 243, 253, 268, 272, 297, 313, 330, 342, 353, 373, 396, 404, 419, 431, 458, 466, 483, 495, 510, 530, 539, 553, 594, 604, 627, 641, 660, 664, 689, 703, 726, 742, 749, 757, 798

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..60.

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