A344033 a(n) = n * Sum_{d|n} d^mu(n/d).

1, 6, 12, 22, 30, 47, 56, 82, 93, 117, 132, 197, 182, 219, 248, 306, 306, 419, 380, 487, 472, 519, 552, 773, 655, 717, 786, 905, 870, 1240, 992, 1154, 1136, 1209, 1272, 1697, 1406, 1503, 1576, 1927, 1722, 2322, 1892, 2125, 2258, 2187, 2256, 2981, 2457, 2857, 2672, 2927

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..52.

Example

a(4) = 4 * Sum_{d|4} d^mu(4/d) = 4 * (1^0 + 2^(-1) + 4^1) = 22.

Mathematica

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

Prog

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

Crossrefs

Cf. A008683 (mu).

Sequence in context: A055458 A360570 A178733 * A266085 A144568 A222001

Adjacent sequences: A344030 A344031 A344032 * A344034 A344035 A344036

Keyword

nonn

Author

Wesley Ivan Hurt, May 24 2021

Status

approved