cp's OEIS Frontend

A365745 Powers s^m, m > 1, where s is a composite squarefree number that is not a primorial.

%I A365745 #47 Dec 11 2023 08:39:25
%S A365745 100,196,225,441,484,676,1000,1089,1156,1225,1444,1521,1764,2116,2601,
%T A365745 2744,3025,3249,3364,3375,3844,4225,4356,4761,4900,5476,5929,6084,
%U A365745 6724,7225,7396,7569,8281,8649,8836,9025,9261,10000,10404,10648,11025,11236,12100,12321
%N A365745 Powers s^m, m > 1, where s is a composite squarefree number that is not a primorial.
%H A365745 Michael De Vlieger, <a href="/A365745/b365745.txt">Table of n, a(n) for n = 1..10000</a>
%F A365745 This sequence is {A303606 \ A365308}.
%F A365745 This sequence contains powers s^m, m > 1, for s in {A120944 \ A002110}.
%e A365745 100 is the first term in this sequence since it is 10^2; 10 is a squarefree composite number. All powers 10^m, m > 1 are in the sequence.
%e A365745 36 is not in the sequence since it is 6^2, where 6 is a product of the smallest 2 primes; none of the powers 6^m, m > 1 are in the sequence.
%t A365745 nn = 2^30; ss = Floor@ Sqrt[nn]; p = 3;
%t A365745 s = Complement[
%t A365745   Select[Range[ss], And[SquareFreeQ[#], CompositeQ[#]] &],
%t A365745   NestWhileList[(Set[p, NextPrime[p]]; # p) &, 6, # <= ss &] ];
%t A365745 Union@ Reap[Do[k = 2; While[s[[i]]^k <= nn, Sow[s[[i]]^k]; k++],
%t A365745   {i, Length[s]}] ][[-1, 1]]
%Y A365745 Cf. A002110, A120944, A303606, A365308.
%K A365745 nonn,easy
%O A365745 1,1
%A A365745 _Michael De Vlieger_, Dec 10 2023