A361177 - OEIS

%I #10 Mar 04 2023 08:56:24

%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 38,39,41,42,43,46,47,48,51,53,55,57,58,59,61,62,65,66,67,69,70,71,73,

%U 74,77,78,79,80,81,82,83,85,86,87,89,91,93,94,95,97,101,102

%N Exponentially powerful numbers: numbers whose exponents in their canonical prime factorization are all powerful numbers (A001694).

%C First differs from it subsequence A197680 at n = 167: a(167) = 256 is not a term of A197680.

%C The asymptotic density of this sequence is Product_{p prime} ((1 - 1/p)*(1 + Sum_{i>=1} 1/p^A001694(i))) = 0.6427901996... .

%H Amiram Eldar, <a href="/A361177/b361177.txt">Table of n, a(n) for n = 1..10000</a>

%t powQ[n_] := n == 1 || Min[FactorInteger[n][[;; , 2]]] > 1; Select[Range[100], AllTrue[FactorInteger[#][[;;, 2]], powQ] &]

%o (PARI) ispow(n) = {n == 1 || vecmin(factor(n)[,2]) > 1; }

%o is(n) = {my(e = factor(n)[, 2]); if(n == 1, return(1)); for(i=1, #e, if(!ispow(e[i]), return(0))); 1;}

%Y Cf. A001694.

%Y Similar sequences: A197680, A209061, A138302, A268335.

%K nonn

%O 1,2

%A _Amiram Eldar_, Mar 03 2023