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%I #11 Aug 12 2015 17:48:52
%S 72,108,200,288,392,500,675,800,864,968,972,1125,1152,1323,1352,1372,
%T 1568,1944,2312,2888,3087,3200,3267,3456,3872,4000,4232,4563,5324,
%U 5408,6075,6125,6272,6728,7688,7803,8575,8748,8788,9248,9747,10952,10976
%N Numbers that factorize into a prime number of distinct prime factors each raised to a different prime exponent.
%H Harvey P. Dale, <a href="/A114128/b114128.txt">Table of n, a(n) for n = 1..600</a>
%t pnpfQ[n_]:=Module[{pn=PrimeNu[n],fi=Transpose[FactorInteger[n]][[2]]}, PrimeQ[ pn]&&Length[Union[fi]]==pn&&AllTrue[fi,PrimeQ]]; Select[Range[ 11000], pnpfQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Aug 12 2015 *)
%o (PARI) isok(n) = {nbf = omega(n); if (! isprime(nbf), return (0)); f = factor(n); for (i = 1, nbf, if (! isprime(f[i, 2]), return (0)); for (j = i+1, nbf, if (f[i, 2] == f[j, 2], return (0)););); return (1);} \\ _Michel Marcus_, Aug 18 2013
%Y Subsequence of A114129.
%K nonn
%O 1,1
%A _Jon Wild_, Feb 14 2006
%E Definition clarified by _Harvey P. Dale_, Aug 12 2015
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