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%I #23 Sep 17 2020 09:01:22
%S 4,8,12,16,18,24,27,32,36,48,54,64,72,80,81,96,108,120,128,144,160,
%T 162,180,192,200,216,240,243,256,270,288,300,320,324,360,384,400,405,
%U 432,448,450,480,486,500,512,540,576,600,640,648,672,675,720,729,750,768
%N Numbers k such that sum of exponents in prime factorization of k (i.e., A001222(k)) is >= each prime divisor of k.
%H Amiram Eldar, <a href="/A113645/b113645.txt">Table of n, a(n) for n = 1..10000</a>
%F A number k is included if A006530(k) <= A001222(k).
%e 12 = 2^2 *3^1. Since the sum of the prime factorization exponents, 2+1 = 3, is >= the largest prime dividing 12, which is 3, then 12 is included in the sequence.
%t fQ[n_] := Block[{f = FactorInteger@n}, Plus @@ Last /@ f >= Max[First /@ f]]; Select[ Range[2, 800], fQ@ # &] (* _Robert G. Wilson v_, Jan 16 2006 *)
%t qu[n_]:=n>1&&Block[{f=Transpose@FactorInteger@n, s}, s=Plus@@f[[2]];s>=Max@f[[1]]]; L ={};Do[If[qu[n], Print[n];AppendTo[L, n]], {n, 1000}];L (* _Giovanni Resta_, Jan 16 2006 *)
%o (PARI) isok(m) = {my(f=factor(m)); #select(x->(x>bigomega(f)), f[,1]~) == 0;} \\ _Michel Marcus_, Sep 17 2020
%Y A proper subset of A068936.
%Y Cf. A001222, A006530.
%K nonn
%O 1,1
%A _Leroy Quet_, Jan 15 2006
%E More terms from _Robert G. Wilson v_ and _Giovanni Resta_, Jan 16 2006
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