A344465 - OEIS

%I #3 May 20 2021 00:34:41

%S 1,3,4,4,6,12,8,5,5,18,12,14,14,24,24,6,18,14,20,20,32,36,24,16,7,42,

%T 6,26,30,72,32,7,48,54,48,17,38,60,56,22,42,96,44,38,26,72,48,18,9,20,

%U 72,44,54,16,72,28,80,90,60,76,62,96,34,8,84,144,68,56,96,144,72

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

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

%e a(10) = Sum_{d|10} d^abs(mu(d)) = 1^1 + 2^1 + 5^1 + 10^1 = 18.

%t Table[Sum[k^Abs[MoebiusMu[k]] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

%Y Cf. A008683 (mu).

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, May 20 2021