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A333449
a(n) = Sum_{k=1..n} prime(floor(n/k)).
1
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
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