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A282668 Numbers m whose greatest divisor <= sqrt(m) is prime. 2

%I

%S 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 50,51,55,56,57,58,62,63,65,69,70,74,75,77,82,84,85,86,87,91,93,94,95,

%U 98,105,106,111,115,118,119,121,122,123,125,129,132,133,134

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

%C The squares of the primes are in the sequence.

%H Amiram Eldar, <a href="/A282668/b282668.txt">Table of n, a(n) for n = 1..10000</a>

%F {n: A033676(n) in A000040}. - _R. J. Mathar_, Feb 23 2017

%e 15 is a term since its biggest divisor <= sqrt(15) is 3 (this is a not sqrt(15)-smooth example).

%e 18 is a term since its biggest divisor <= sqrt(18) is 3 (this is a sqrt(18)-smooth example).

%e 24 is not a term since its biggest divisor <= sqrt(24) is 4 (this is a sqrt(24)-smooth counterexample).

%e 42 is not a term since its biggest divisor <= sqrt(42) is 6 (this is a not sqrt(42)-smooth counterexample).

%t f[m_]:=Module[{A=Divisors[m],a},a=Length[A];A[[Floor[(a+1)/2]]]];

%t Select[Range[176],PrimeQ[f[#]]&]

%Y Cf. A048098, A064052.

%K nonn

%O 1,1

%A _Emmanuel Vantieghem_, Feb 20 2017

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Last modified April 11 02:27 EDT 2021. Contains 342886 sequences. (Running on oeis4.)