id:A112400 - OEIS Search Results

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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, 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; listen)

	OFFSET	`1,6`
	COMMENT	`The justification for a(1) being 0 is that the sum is empty.`
	LINKS	`Leroy Quet, Home Page (listed in lieu of email address)`
	EXAMPLE	`12 = 2^3 * 3^1. So a(12) = mu(3) + mu(1) = -1 + 1 = 0.`
	PROGRAM	`(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)`
	CROSSREFS	`Cf. A008683.` `Sequence in context: A035180 A163819 A092673 this_sequence A116861 A105242 A114116` `Adjacent sequences: A112397 A112398 A112399 this_sequence A112401 A112402 A112403`
	KEYWORD	`sign`
	AUTHOR	`Leroy Quet, Dec 06 2005`
	EXTENSIONS	`More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Dec 09 2005`

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Last modified December 19 12:50 EST 2009. Contains 171053 sequences.

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