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A333450

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

2, 1, 1, 2, 4, 5, 7, 7, 9, 12, 12, 15, 17, 16, 16, 20, 24, 22, 26, 23, 21, 26, 28, 28, 32, 33, 31, 32, 32, 29, 41, 39, 43, 40, 44, 40, 44, 45, 45, 47, 51, 52, 60, 55, 53, 52, 62, 64, 64, 56, 54, 55, 55, 65, 67, 69, 69, 70, 74, 73, 73, 70, 80, 80, 76, 69, 81, 84, 90, 81, 83, 87, 93, 94

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..74.

FORMULA

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

MATHEMATICA

Table[Sum[MoebiusMu[k] Prime[Floor[n/k]], {k, 1, n}], {n, 1, 74}]

g[1] = 2; g[n_] := Prime[n] - Prime[n - 1]; a[n_] := Sum[Sum[MoebiusMu[k/d] g[d], {d, Divisors[k]}], {k, 1, n}]; Table[a[n], {n, 1, 74}]

PROG

(PARI) a(n) = sum(k=1, n, moebius(k)*prime(n\k)); \\ Michel Marcus, Mar 22 2020