%I #7 Jun 08 2021 07:32:16
%S 1,2,3,8,1,6,7,16,10,1,11,24,1,14,15,33,1,36,1,21,1,22,23,48,2,1,28,
%T 29,1,30,31,65,1,34,35,144,1,38,39,80,1,42,43,88,46,1,47,97,50,2,1,53,
%U 1,108,1,57,1,58,59,120,1,62,64,67,1,66,67,136,1,70,71,288,1,74,150
%N a(n) = Sum_{d^2|n} n^abs(mu(n-d)).
%F If p is prime, a(p) = Sum_{d^2|p} p^abs(mu(p-d)) = p^abs(mu(p-1)).
%e a(8) = Sum_{d^2|8} 8^abs(mu(8-d)) = 8^abs(mu(7)) + 8^abs(mu(6)) = 8^1 + 8^1 = 16.
%t Table[Sum[n^(MoebiusMu[n - k]^2) (1 - Ceiling[n/k^2] + Floor[n/k^2]), {k, n}], {n, 100}]
%o (PARI) a(n) = if (n==1, 1, sumdiv(n, d, if (issquare(d), n^abs(moebius(n-sqrtint(d)))))); \\ _Michel Marcus_, Jun 08 2021
%Y Cf. A008683 (mu).
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, Jun 07 2021