id:A085021 - OEIS Search Results

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Number of prime factors of cyclotomic(n,2), which is A019320(n), the value of the n-th cyclotomic polynomial evaluated at x=2.

+0
10

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 2, 1, 2, 3, 3, 3, 2, 3, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 3, 1, 2, 3, 2, 3, 2, 2, 3, 1, 1, 3, 1, 3, 2, 2, 2, 1, 1, 2, 2, 1, 1, 3, 4, 1, 2, 3, 2, 2, 1, 3, 4 (list; graph; listen)

	OFFSET	`1,11`
	COMMENT	`The Mobius transform of this sequence yields A046051, the number of prime factors of Mersenne number 2^n-1.` `The number of prime factors in the primitive part of 2^n-1. - T. D. Noe, Jul 19 2008`
	LINKS	`T. D. Noe, Table of n, a(n) for n=1..500` `H. Mishima, Factorization of Cyclotomic Numbers` `Eric Weisstein's World of Mathematics, Cyclotomic Polynomial` `Eric Weisstein's World of Mathematics, Mobius Transform`
	EXAMPLE	`a(11) = 2 because cyclotomic(11,2) = 2047, which has two factors: 23 and 89.`
	MATHEMATICA	`Join[{0}, Table[Plus@@Transpose[FactorInteger[Cyclotomic[n, 2]]][[2]], {n, 2, 100}]]`
	CROSSREFS	`Cf. A019320, A046051.` `Adjacent sequences: A085018 A085019 A085020 this_sequence A085022 A085023 A085024` `Sequence in context: A078572 A122750 A030421 this_sequence A060209 A037830 A139039`
	KEYWORD	`nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Jun 19 2003`

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Last modified October 13 02:37 EDT 2008. Contains 145008 sequences.

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