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A008481
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If n = Product (p_j^k_j) then a(n) = Sum partition(k_j).
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5
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0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 5, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 7, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 6, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 4, 1, 2, 3, 11, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 3, 3, 2, 3, 1, 6, 5, 2, 1, 4, 2, 2, 2
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B + C), where B is Mertens's constant (A077761) and C = Sum_{p prime} f(1/p) = 1.03089282973521424158..., where f(x) = -1 + (1-x) * Product_{k>=1} (1 + x^k)/(1 - x^(2*k)). - Amiram Eldar, Sep 29 2023
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MAPLE
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a:= n-> add(combinat[numbpart](i[2]), i=ifactors(n)[2]):
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MATHEMATICA
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Prepend[ Array[ Plus @@ (PartitionsP /@ Last[ Transpose[ FactorInteger[ # ] ] ])&, 100, 2 ], 0 ]
(* Second program: *)
Array[Total[PartitionsP /@ FactorInteger[#][[All, -1]] - Boole[# == 1]] &, 87] (* Michael De Vlieger, Sep 02 2018 *)
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PROG
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CROSSREFS
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Differs from A318473 for the first time at n=32, where a(32)=7, while A318473(32)=8.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Term a(1) corrected from 1 to 0 (for an empty sum) by Antti Karttunen, Aug 30 2018
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STATUS
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approved
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