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%I #13 May 04 2023 12:30:45
%S 0,1,1,-1,1,2,1,-1,-1,2,1,0,1,2,2,0,1,0,1,0,2,2,1,0,-1,2,-1,0,1,3,1,
%T -1,2,2,2,-2,1,2,2,0,1,3,1,0,0,2,1,1,-1,0,2,0,1,0,2,0,2,2,1,1,1,2,0,1,
%U 2,3,1,0,2,3,1,-2,1,2,0,0,2,3,1,1,0,2,1,1,2,2,2,0,1,1,2,0,2,2,2,0,1,0,0,-2,1,3,1,0,3,2,1,-2,1,3,2,1,1,3,2,0,0,2,2,1,-1,2
%N a(n) = Sum_{p|n, p prime} mu(b(p,n)), where mu(k) = A008683(k) (the Moebius function) and p^b(p,n) is the highest power of the prime p dividing n.
%C The justification for a(1) being 0 is that the sum is empty.
%H Antti Karttunen, <a href="/A112400/b112400.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%e 12 = 2^3 * 3^1. So a(12) = mu(3) + mu(1) = -1 + 1 = 0.
%o (PARI) a(n)=local(v,i,s);v=factor(n);s=0;for(i=1,matsize(v)[1],s+=moebius(v[i,2]));s \\ (Herrgesell)
%o (PARI) A112400(n) = vecsum(apply(e -> moebius(e), factorint(n)[, 2])); \\ _Antti Karttunen_, Jul 07 2017
%Y Cf. A008683.
%K sign
%O 1,6
%A _Leroy Quet_, Dec 06 2005
%E More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Dec 09 2005
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