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

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}]

Crossrefs

Cf. A000040, A001223, A007444, A008683, A030013, A054541, A182986, A333450 (partial sums).

Sequence in context: A349815 A173389 A241062 * A360711 A284620 A038698

Adjacent sequences: A333468 A333469 A333470 * A333472 A333473 A333474

Keyword

sign

Author

Ilya Gutkovskiy, Mar 23 2020

Status

approved