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%I #21 Aug 03 2014 14:01:29
%S 21,33,57,69,85,93,105,129,133,145,177,195,205,213,217,231,237,249,
%T 253,265,309,393,417,445,465,469,483,489,493,505,517,553,565,573,597,
%U 609,627,633,645,663,669,685,697,753,781,793,813,817,861,865
%N Composite squarefree numbers whose average prime factor is a prime number.
%H Charles R Greathouse IV, <a href="/A187073/b187073.txt">Table of n, a(n) for n = 1..10000</a>
%e 195 = 3 * 5 * 13, and the average is (3 +5 +13) / 3 = 21 / 3 = 7, also a prime.
%t okQ[n_] := Module[{p, e}, {p, e} = Transpose[FactorInteger[n]]; ! PrimeQ[n] && Max[e] == 1 && PrimeQ[Mean[p]]]; Select[Range[1000], okQ] (* _T. D. Noe_, Mar 03 2011 *)
%o (PARI) isA187073(n)=my(f=factor(n));#f[,1]>1&vecmax(f[,2])==1&denominator(f=sum(i=1,#f[,1],f[i,1])/#f[,1])==1&isprime(f) \\ _Charles R Greathouse IV_, Jun 12 2011
%K nonn
%O 1,1
%A _Antonio Roldán_, Mar 03 2011
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