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 A069352 Total number of prime factors of 3-smooth numbers. 14
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) = A001222(A003586(n)); a(n) = A022328(n) + A022329(n); A086414(n) <= A086415(n) <= a(n). LINKS Zak Seidov, Table of n, a(n) for n = 1..10000 FORMULA a(n) = i+j for 3-smooth numbers n = 2^i*3^j (A003586). a(n) = A001222(A033845(n))-2. - Enrique Pérez Herrero, Jan 04 2012 MATHEMATICA 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 *) PROG (Haskell) a069352 = a001222 . a003586  -- Reinhard Zumkeller, May 16 2015 CROSSREFS Cf. A003586, A001222, A003586, A022328, A022329, A086414, A086415. Sequence in context: A115727 A115726 A086413 * A073453 A123229 A127095 Adjacent sequences:  A069349 A069350 A069351 * A069353 A069354 A069355 KEYWORD nonn AUTHOR Reinhard Zumkeller, Mar 18 2002 EXTENSIONS Edited by N. J. A. Sloane, Oct 27 2008 at the suggestion of R. J. Mathar. STATUS approved

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