A344575 - OEIS

%I #3 May 23 2021 16:50:26

%S 1,3,4,7,6,12,8,14,13,18,12,26,14,24,24,27,18,38,20,38,32,36,24,52,31,

%T 42,38,50,30,72,32,52,48,54,48,77,38,60,56,76,42,96,44,74,74,72,48,

%U 102,57,92,72,86,54,112,72,100,80,90,60,148,62,96,98,101,84,144,68,110,96

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

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

%F a(8) = Sum_{d|8} d^abs(mu(8/d)) = 1^0 + 2^0 + 4^1 + 8^1 = 14.

%t Table[Sum[k^Abs[MoebiusMu[n/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 23 2021