A344033 - OEIS

%I #25 May 25 2021 08:07:05

%S 1,6,12,22,30,47,56,82,93,117,132,197,182,219,248,306,306,419,380,487,

%T 472,519,552,773,655,717,786,905,870,1240,992,1154,1136,1209,1272,

%U 1697,1406,1503,1576,1927,1722,2322,1892,2125,2258,2187,2256,2981,2457,2857,2672,2927

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

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

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

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

%o (PARI) a(n) = n*sumdiv(n, d, d^moebius(n/d)); \\ _Michel Marcus_, May 25 2021

%Y Cf. A008683 (mu).

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, May 24 2021