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A282668 Numbers m whose greatest divisor <= sqrt(m) is prime.

%I A282668 #16 Apr 11 2020 08:03:29
%S A282668 4,6,8,9,10,12,14,15,18,21,22,25,26,27,30,33,34,35,38,39,40,45,46,49,
%T A282668 50,51,55,56,57,58,62,63,65,69,70,74,75,77,82,84,85,86,87,91,93,94,95,
%U A282668 98,105,106,111,115,118,119,121,122,123,125,129,132,133,134
%N A282668 Numbers m whose greatest divisor <= sqrt(m) is prime.
%C A282668 The squares of the primes are in the sequence.
%H A282668 Amiram Eldar, <a href="/A282668/b282668.txt">Table of n, a(n) for n = 1..10000</a>
%F A282668 {n: A033676(n) in A000040}. - _R. J. Mathar_, Feb 23 2017
%e A282668 15 is a term since its biggest divisor <= sqrt(15) is 3 (this is a not sqrt(15)-smooth example).
%e A282668 18 is a term since its biggest divisor <= sqrt(18) is 3 (this is a sqrt(18)-smooth example).
%e A282668 24 is not a term since its biggest divisor <= sqrt(24) is 4 (this is a sqrt(24)-smooth counterexample).
%e A282668 42 is not a term since its biggest divisor <= sqrt(42) is 6 (this is a not sqrt(42)-smooth counterexample).
%t A282668 f[m_]:=Module[{A=Divisors[m],a},a=Length[A];A[[Floor[(a+1)/2]]]];
%t A282668 Select[Range[176],PrimeQ[f[#]]&]
%Y A282668 Cf. A048098, A064052.
%K A282668 nonn
%O A282668 1,1
%A A282668 _Emmanuel Vantieghem_, Feb 20 2017