A308966 Integers k > 1 whose least prime factor is greater than log_2(k).

2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 119, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 209, 211, 221, 223, 227, 229, 233

Offset: 1

Author

Robert Israel, Jul 03 2019

Keywords

• nonn

Comments

p^k is a member if p is prime and 1 <= k < p/log_2(p).

p*q is a member if p and q are primes and p < q < 2^p/p.

Examples

			a(24) = 77 is a member because its least prime factor is 7, and 7 > log_2(77) ~= 6.2668.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020639.

Programs

Magma

[k:k in [2..250]| PrimeDivisors(k)[1] gt Log(2,k)]; // Marius A. Burtea, Jul 03 2019

Maple

filter:= proc(n) 2^min(numtheory:-factorset(n)) > n end proc:
select(filter, [$2..1000]);

Mathematica

filterQ[n_] := FactorInteger[n][[1, 1]] > Log[2, n];
Select[Range[2, 1000], filterQ] (* Jean-François Alcover, Jul 31 2020 *)