id:A087073 - OEIS Search Results

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Mobius transform of A051664, the number of nonzero terms in the n-th cyclotomic polynomial.

+0
2

2, 0, 1, 0, 3, 0, 5, 0, 0, 0, 9, 0, 11, 0, 1, 0, 15, 0, 17, 0, 1, 0, 21, 0, 0, 0, 0, 0, 27, 0, 29, 0, 3, 0, 7, 0, 35, 0, 3, 0, 39, 0, 41, 0, 0, 0, 45, 0, 0, 0, 5, 0, 51, 0, 3, 0, 5, 0, 57, 0, 59, 0, 0, 0, 15, 0, 65, 0, 7, 0, 69, 0, 71, 0, 0, 0, 15, 0, 77, 0, 0, 0, 81, 0, 21, 0, 9, 0, 87, 0, 5, 0, 9, 0, 9 (list; graph; listen)

	OFFSET	`1,1`
	COMMENT	`Note that a(n) = 0 for even n and a(n) = n-2 for prime n. It appears that the following are true: a(1) is the only positive even term, all odd numbers eventually appear in the sequence, a(n) = 0 if n is squareful and a(n) > 0 if n is squarefree. Assuming the truth of the last statement, we can show that if distinct odd primes p and q divide n, then A051664(n) > p + q - 2.`
	LINKS	`T. D. Noe, Table of n, a(n) for n=1..1000`
	FORMULA	`a(n) = Sum{d\|n} mu(n/d) A051664(d)`
	CROSSREFS	`Cf. A051664.` `Sequence in context: A104477 A052173 A124305 this_sequence A106844 A125989 A125924` `Adjacent sequences: A087070 A087071 A087072 this_sequence A087074 A087075 A087076`
	KEYWORD	`nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Aug 08 2003`
	EXTENSIONS	`Definition corrected: "inverse moebius transform" to "moebius transform" by Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jan 17 2009`

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Last modified March 20 09:10 EDT 2010. Contains 173642 sequences.

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