A343876 a(n) = n * Sum_{d|n} d^mu(d).

1, 3, 4, 10, 6, 47, 8, 28, 21, 117, 12, 118, 14, 219, 248, 72, 18, 177, 20, 274, 472, 519, 24, 284, 55, 717, 90, 494, 30, 992, 32, 176, 1136, 1209, 1272, 462, 38, 1503, 1576, 628, 42, 1806, 44, 1126, 834, 2187, 48, 664, 105, 685, 2672, 1538, 54, 639, 3096, 1100, 3328, 3453

Offset

1,2

Comments

If p is prime, a(p) = p * Sum_{d|p} d^mu(d) = p * (1^1 + p^(-1)) = p * (1 + 1/p) = p + 1.

Links

Table of n, a(n) for n=1..58.

Example

a(6) = 6 * Sum_{d|6} d^mu(d) = 6 * (1^1 + 2^(-1) + 3^(-1) + 6^1) = 47.

Mathematica

Table[n*Sum[i^MoebiusMu[i] (1 - Ceiling[n/i] + Floor[n/i]), {i, n}], {n, 80}]

Prog

(PARI) a(n) = n*sumdiv(n, d, d^moebius(d)); \\ Michel Marcus, May 25 2021

Crossrefs

Cf. A008683 (mu).

Sequence in context: A023896 A328711 A361655 * A356150 A222136 A339652

Adjacent sequences: A343873 A343874 A343875 * A343877 A343878 A343879

Keyword

nonn

Author

Wesley Ivan Hurt, May 24 2021

Status

approved