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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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6
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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
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OFFSET
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1,2
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COMMENTS
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Same as A014963, except this function is zero when n is not a prime power, whereas A014963 is one.
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LINKS
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FORMULA
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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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MATHEMATICA
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Table[If[Length@ # == 1, #[[1, 1]], 0] &@ FactorInteger@ n, {n, 96}] /. 1 -> 0 (* Michael De Vlieger, Jun 19 2016 *)
Table[If[PrimePowerQ[n], FactorInteger[n][[1, 1]], 0], {n, 100}] (* Harvey P. Dale, Jan 25 2020 *)
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PROG
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(Haskell)
a120007 1 = 0
a120007 n | until ((> 0) . (`mod` spf)) (`div` spf) n == 1 = spf
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where spf = a020639 n
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CROSSREFS
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Cf. A000040, A001414, A007947, A014963, A010051, A010055, A061397, A070939, A140508 (Möbius transform of this sequence), A297108, A297109.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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