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 A342694 a(n) = Sum_{d|n} d * mu(d) * floor(n/d^2). 0

%I #5 May 18 2021 17:48:21

%S 1,2,3,2,5,4,7,4,6,6,11,3,13,8,12,8,17,4,19,10,15,12,23,6,20,14,18,14,

%T 29,2,31,16,24,18,30,12,37,20,27,15,41,16,43,22,25,24,47,15,42,16,36,

%U 26,53,16,45,21,39,30,59,8,61,32,35,32,55,19,67,34,48,19,71,24,73,38

%N a(n) = Sum_{d|n} d * mu(d) * floor(n/d^2).

%C If p is prime, a(p) = Sum_{d|p} d * mu(d) * floor(p/d^2) = 1*1*p + p*(-1)*0 = p.

%e a(10) = Sum_{d|10} d * mu(d) * floor(10/d^2) = 1*1*10 + 2*(-1)*2 + 5*(-1)*0 + 10*1*0 = 6.

%t Table[Sum[k*MoebiusMu[k] Floor[n/k^2] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]

%Y Cf. A008683 (mu).

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, May 18 2021

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Last modified December 1 03:32 EST 2023. Contains 367468 sequences. (Running on oeis4.)