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

100, 196, 225, 441, 484, 676, 1000, 1089, 1156, 1225, 1444, 1521, 1764, 2116, 2601, 2744, 3025, 3249, 3364, 3375, 3844, 4225, 4356, 4761, 4900, 5476, 5929, 6084, 6724, 7225, 7396, 7569, 8281, 8649, 8836, 9025, 9261, 10000, 10404, 10648, 11025, 11236, 12100, 12321

Offset: 1

Author

Michael De Vlieger, Dec 10 2023

Keywords

• nonn
• easy

Examples

			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.
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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A120944, A303606, A365308.

Programs

Mathematica

nn = 2^30; ss = Floor@ Sqrt[nn]; p = 3;
s = Complement[
  Select[Range[ss], And[SquareFreeQ[#], CompositeQ[#]] &],
  NestWhileList[(Set[p, NextPrime[p]]; # p) &, 6, # <= ss &] ];
Union@ Reap[Do[k = 2; While[s[[i]]^k <= nn, Sow[s[[i]]^k]; k++],
  {i, Length[s]}] ][[-1, 1]]

Formula

This sequence is {A303606 \ A365308}.

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