A333471 - OEIS

A333471

a(n) = 2 * mu(n) + Sum_{d|n, d > 1} mu(n/d) * (prime(d) - prime(d-1)).

2, -1, 0, 1, 2, 1, 2, 0, 2, 3, 0, 3, 2, -1, 0, 4, 4, -2, 4, -3, -2, 5, 2, 0, 4, 1, -2, 1, 0, -3, 12, -2, 4, -3, 4, -4, 4, 1, 0, 2, 4, 1, 8, -5, -2, -1, 10, 2, 0, -8, -2, 1, 0, 10, 2, 2, 0, 1, 4, -1, 0, -3, 10, 0, -4, -7, 12, 3, 6, -9, 2, 4, 6, 1, -2, -3, 2, 3, 2, -2

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OFFSET

1,1

COMMENTS

Moebius transform of A054541 (2 followed by prime gaps).

LINKS

Table of n, a(n) for n=1..80.

FORMULA

a(n) = Sum_{d|n} mu(n/d) * A054541(d).

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

MATHEMATICA

a[n_] := 2 MoebiusMu[n] + Sum[If[d > 1, MoebiusMu[n/d] (Prime[d] - Prime[d - 1]), 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 80}]