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A120007 Mobius transform of sum of prime factors of n with multiplicity (A001414). 5
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; text; internal format)
OFFSET

1,2

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). [Reinhard Zumkeller, Mar 26 2010]

a(n) = A064911(A007947(n)). [Reinhard Zumkeller, Sep 19 2011]

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.

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).

a(n) = Sum_{k=2..n} k*A010051(k)*(floor(k^n/n)-floor((k^n -1)/n)). - Anthony Browne, Jun 17 2016

MATHEMATICA

Table[If[Length@ # == 1, #[[1, 1]], 0] &@ FactorInteger@ n, {n, 96}] /. 1 -> 0 (* Michael De Vlieger, Jun 19 2016 *)

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

CROSSREFS

Cf. A001414, A014963, A010051.

Sequence in context: A022662 A059051 A130069 * A092509 A214053 A214056

Adjacent sequences:  A120004 A120005 A120006 * A120008 A120009 A120010

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, Jun 02 2006

STATUS

approved

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Last modified December 6 06:58 EST 2016. Contains 278775 sequences.