A365745 - OEIS

%I #47 Dec 11 2023 08:39:25

%S 100,196,225,441,484,676,1000,1089,1156,1225,1444,1521,1764,2116,2601,

%T 2744,3025,3249,3364,3375,3844,4225,4356,4761,4900,5476,5929,6084,

%U 6724,7225,7396,7569,8281,8649,8836,9025,9261,10000,10404,10648,11025,11236,12100,12321

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

%H Michael De Vlieger, <a href="/A365745/b365745.txt">Table of n, a(n) for n = 1..10000</a>

%F This sequence is {A303606 \ A365308}.

%F This sequence contains powers s^m, m > 1, for s in {A120944 \ A002110}.

%e 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 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 nn = 2^30; ss = Floor@ Sqrt[nn]; p = 3;

%t s = Complement[

%t   Select[Range[ss], And[SquareFreeQ[#], CompositeQ[#]] &],

%t   NestWhileList[(Set[p, NextPrime[p]]; # p) &, 6, # <= ss &] ];

%t Union@ Reap[Do[k = 2; While[s[[i]]^k <= nn, Sow[s[[i]]^k]; k++],

%t   {i, Length[s]}] ][[-1, 1]]

%Y Cf. A002110, A120944, A303606, A365308.

%K nonn,easy

%O 1,1

%A _Michael De Vlieger_, Dec 10 2023