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A069352
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Total number of prime factors of 3-smooth numbers.
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14
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0, 1, 1, 2, 2, 3, 2, 3, 4, 3, 4, 3, 5, 4, 5, 4, 6, 5, 4, 6, 5, 7, 6, 5, 7, 6, 5, 8, 7, 6, 8, 7, 6, 9, 8, 7, 6, 9, 8, 7, 10, 9, 8, 7, 10, 9, 8, 11, 7, 10, 9, 8, 11, 10, 9, 12, 8, 11, 10, 9, 12, 8, 11, 10, 13, 9, 12, 11, 10, 13, 9, 12, 11, 14, 10, 13, 9, 12, 11, 14, 10, 13, 12, 15, 11
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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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a(n) = i+j for 3-smooth numbers n = 2^i*3^j (A003586).
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MATHEMATICA
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smoothNumbers[p_, max_] := Module[{a, aa, k, pp, iter}, k = PrimePi[p]; aa = Array[a, k]; pp = Prime[Range[k]]; iter = Table[{a[j], 0, PowerExpand @ Log[pp[[j]], max/Times @@ (Take[pp, j-1]^Take[aa, j-1])]}, {j, 1, k}]; Table[Times @@ (pp^aa), Sequence @@ iter // Evaluate] // Flatten // Sort]; PrimeOmega /@ smoothNumbers[3, 10^5] (* Jean-François Alcover, Nov 11 2016 *)
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PROG
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(Haskell)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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