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A112400
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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.
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0
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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; internal format)
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OFFSET
| 1,6
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COMMENTS
| The justification for a(1) being 0 is that the sum is empty.
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EXAMPLE
| 12 = 2^3 * 3^1. So a(12) = mu(3) + mu(1) = -1 + 1 = 0.
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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)
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CROSSREFS
| Cf. A008683.
Sequence in context: A035180 A163819 A092673 * A116861 A105242 A114116
Adjacent sequences: A112397 A112398 A112399 * A112401 A112402 A112403
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KEYWORD
| sign
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AUTHOR
| Leroy Quet, Dec 06 2005
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EXTENSIONS
| More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Dec 09 2005
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