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A069352 Total number of prime factors of 3-smooth numbers.

%I A069352 #21 Apr 09 2018 02:49:25
%S A069352 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,
%T A069352 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,
%U A069352 10,13,9,12,11,10,13,9,12,11,14,10,13,9,12,11,14,10,13,12,15,11
%N A069352 Total number of prime factors of 3-smooth numbers.
%C A069352 a(n) = A001222(A003586(n));
%C A069352 a(n) = A022328(n) + A022329(n);
%C A069352 A086414(n) <= A086415(n) <= a(n).
%H A069352 Zak Seidov, <a href="/A069352/b069352.txt">Table of n, a(n) for n = 1..10000</a>
%F A069352 a(n) = i+j for 3-smooth numbers n = 2^i*3^j (A003586).
%F A069352 a(n) = A001222(A033845(n))-2. - _Enrique Pérez Herrero_, Jan 04 2012
%t A069352 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 *)
%o A069352 (Haskell)
%o A069352 a069352 = a001222 . a003586  -- _Reinhard Zumkeller_, May 16 2015
%Y A069352 Cf. A003586, A001222, A003586, A022328, A022329, A086414, A086415.
%K A069352 nonn
%O A069352 1,4
%A A069352 _Reinhard Zumkeller_, Mar 18 2002
%E A069352 Edited by _N. J. A. Sloane_, Oct 27 2008 at the suggestion of _R. J. Mathar_.