A274034 - OEIS

%I #32 Jul 05 2016 19:42:42

%S 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 38,39,41,42,43,46,47,48,51,53,55,57,58,59,61,62,64,65,66,67,69,70,71,

%U 73,74,77,78,79,80,81,82,83,85,86,87,89,91,93,94,95,97

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

%C The density of this sequence is 0.6504456084..., see A273487. - _Charles R Greathouse IV_, Jul 01 2016

%H Alois P. Heinz, <a href="/A274034/b274034.txt">Table of n, a(n) for n = 1..10000</a>

%H Alec Jones, <a href="/A274034/a274034.txt">Java program</a>

%e 8 is not present in this sequence because 8 = 2^3 and 3 is prime.

%e 96 is not present in this sequence because 96 = 2^5*3^1 and 5 is prime.

%p a:= proc(n) option remember; local k; for k from

%p       `if`(n=1, 1, a(n-1)+1) while ormap(i->

%p        isprime(i[2]), ifactors(k)[2]) do od; k

%p     end:

%p seq(a(n), n=1..80);  # _Alois P. Heinz_, Jun 30 2016

%t 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 (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 Cf. A056166 (exponents are prime), A197680 (exponents are squares).

%K nonn,easy

%O 1,2

%A _Alec Jones_, Jun 07 2016