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A120007
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Mobius transform of sum of prime factors of n with multiplicity (A001414).
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5
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Same as A014963, except this function is zero when n is not a prime power, whereas A014963 is one.
a(n) = A010055(n)*A007947(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 26 2010]
a(n) = A064911(A007947(n)). [Reinhard Zumkeller, Sep 19 2011]
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Prime Factor.
Eric Weisstein's World of Mathematics, Prime Zeta Function.
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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).
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PROG
| (Haskell)
a120007 1 = 0
a120007 n | until ((> 0) . (`mod` spf)) (`div` spf) n == 1 = spf
| otherwise = 0
where spf = a020639 n
-- Reinhard Zumkeller, Sep 19 2011
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CROSSREFS
| Cf. A001414, A014963.
Sequence in context: A022662 A059051 A130069 * A092509 A014973 A157753
Adjacent sequences: A120004 A120005 A120006 * A120008 A120009 A120010
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KEYWORD
| nonn
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AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 02 2006
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