id:A120007 - OEIS Search Results

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A120007

Mobius transform of sum of prime factors of n with multiplicity (A001414).

+0
4

0, 2, 3, 2, 5, 0, 7, 2, 3, 0, 11, 0, 13, 0, 0, 2, 17, 0, 19, 0, 0, 0, 23, 0, 5, 0, 3, 0, 29, 0, 31, 2, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 0, 0, 47, 0, 7, 0, 0, 0, 53, 0, 0, 0, 0, 0, 59, 0, 61, 0, 0, 2, 0, 0, 67, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 3, 0, 83, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`Same as A014963, except this function is zero when n is not a prime power, whereas A014963 is one.`
	LINKS	`Eric Weisstein's World of Mathematics, Prime Factor.` `Eric Weisstein's World of Mathematics, Prime Zeta Function.`
	FORMULA	`If n is a prime power p^k, k>0, a(n) = p; otherwise a(n) = 0. Dirichlet g.f. sum_{p prime} p/(p^s-1) = sum_{k>0} primezeta(ks-1).`
	CROSSREFS	`Cf. A001414, A014963.` `Adjacent sequences: A120004 A120005 A120006 this_sequence A120008 A120009 A120010` `Sequence in context: A022662 A059051 A130069 this_sequence A092509 A014973 A020500`
	KEYWORD	`nonn`
	AUTHOR	`Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 02 2006`

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Last modified October 11 13:47 EDT 2008. Contains 144830 sequences.

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