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A345276 a(n) = Sum_{d|n} (n-d)^abs(mu(n/d)). 0

%I

%S 0,1,2,3,4,12,6,6,7,22,10,26,12,32,36,11,16,38,18,46,52,52,22,52,21,

%T 62,20,66,28,168,30,20,84,82,92,77,36,92,100,92,40,240,42,106,110,112,

%U 46,102,43,112,132,126,52,112,148,132,148,142,58,340,60,152,158,37,176,384,66

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

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

%e a(12) = Sum_{d|12} (12-d)^abs(mu(12/d)) = 11^0 + 10^1 + 9^0 + 8^1 + 6^1 + 0^1 = 26.

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

%Y Cf. A008683 (mu).

%K nonn

%O 1,3

%A _Wesley Ivan Hurt_, Jun 12 2021

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Last modified May 16 17:38 EDT 2022. Contains 353719 sequences. (Running on oeis4.)