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A274034 Numbers whose exponents in their prime power factorizations are not primes.

%I A274034 #32 Jul 05 2016 19:42:42
%S A274034 1,2,3,5,6,7,10,11,13,14,15,16,17,19,21,22,23,26,29,30,31,33,34,35,37,
%T A274034 38,39,41,42,43,46,47,48,51,53,55,57,58,59,61,62,64,65,66,67,69,70,71,
%U A274034 73,74,77,78,79,80,81,82,83,85,86,87,89,91,93,94,95,97
%N A274034 Numbers whose exponents in their prime power factorizations are not primes.
%C A274034 The density of this sequence is 0.6504456084..., see A273487. - _Charles R Greathouse IV_, Jul 01 2016
%H A274034 Alois P. Heinz, <a href="/A274034/b274034.txt">Table of n, a(n) for n = 1..10000</a>
%H A274034 Alec Jones, <a href="/A274034/a274034.txt">Java program</a>
%e A274034 8 is not present in this sequence because 8 = 2^3 and 3 is prime.
%e A274034 96 is not present in this sequence because 96 = 2^5*3^1 and 5 is prime.
%p A274034 a:= proc(n) option remember; local k; for k from
%p A274034       `if`(n=1, 1, a(n-1)+1) while ormap(i->
%p A274034        isprime(i[2]), ifactors(k)[2]) do od; k
%p A274034     end:
%p A274034 seq(a(n), n=1..80);  # _Alois P. Heinz_, Jun 30 2016
%t A274034 lst0={};Do[lst[n]=Transpose[FactorInteger[n]][[2]]; k=1;While[!(PrimeQ[lst[n][[k]]]||k==Length[lst[n]]), k++]; If[k==Length[lst[n]]&&!PrimeQ[Last[lst[n]]], AppendTo[lst0, n]], {n, 91}]; lst0 (* _Waldemar Puszkarz_, Jun 09 2016 *)
%o A274034 (PARI) isok(n)=my(f = factor(n)); for (k=1, #f~, if (isprime(f[k,2]), return (0));); 1; \\ _Michel Marcus_, Jun 07 2016
%Y A274034 Cf. A056166 (exponents are prime), A197680 (exponents are squares).
%K A274034 nonn,easy
%O A274034 1,2
%A A274034 _Alec Jones_, Jun 07 2016