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A365745
Powers s^m, m > 1, where s is a composite squarefree number that is not a primorial.
1
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
1,1
LINKS
FORMULA
This sequence is {A303606 \ A365308}.
This sequence contains powers s^m, m > 1, for s in {A120944 \ A002110}.
EXAMPLE
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.
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]]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Dec 10 2023
STATUS
approved