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 A112400 a(n) = sum{p=primes,p|n} 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. 1
 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, -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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS The justification for a(1) being 0 is that the sum is empty. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 EXAMPLE 12 = 2^3 * 3^1. So a(12) = mu(3) + mu(1) = -1 + 1 = 0. PROG (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) (PARI) A112400(n) = vecsum(apply(e -> moebius(e), factorint(n)[, 2])); \\ Antti Karttunen, Jul 07 2017 CROSSREFS Cf. A008683. Sequence in context: A337683 A092673 A243842 * A316523 A219185 A116861 Adjacent sequences: A112397 A112398 A112399 * A112401 A112402 A112403 KEYWORD sign AUTHOR Leroy Quet, Dec 06 2005 EXTENSIONS More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Dec 09 2005 STATUS approved

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Last modified March 26 23:26 EDT 2023. Contains 361553 sequences. (Running on oeis4.)