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

4, 6, 8, 9, 10, 12, 14, 15, 18, 21, 22, 25, 26, 27, 30, 33, 34, 35, 38, 39, 40, 45, 46, 49, 50, 51, 55, 56, 57, 58, 62, 63, 65, 69, 70, 74, 75, 77, 82, 84, 85, 86, 87, 91, 93, 94, 95, 98, 105, 106, 111, 115, 118, 119, 121, 122, 123, 125, 129, 132, 133, 134

Offset

1,1

Comments

The squares of the primes are in the sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

{n: A033676(n) in A000040}. - R. J. Mathar, Feb 23 2017

Example

15 is a term since its biggest divisor <= sqrt(15) is 3 (this is a not sqrt(15)-smooth example).
18 is a term since its biggest divisor <= sqrt(18) is 3 (this is a sqrt(18)-smooth example).
24 is not a term since its biggest divisor <= sqrt(24) is 4 (this is a sqrt(24)-smooth counterexample).
42 is not a term since its biggest divisor <= sqrt(42) is 6 (this is a not sqrt(42)-smooth counterexample).

Mathematica

f[m_]:=Module[{A=Divisors[m], a}, a=Length[A]; A[[Floor[(a+1)/2]]]];
Select[Range[176], PrimeQ[f[#]]&]

Crossrefs

Cf. A048098, A064052.

Sequence in context: A323521 A063989 A168645 * A117097 A077135 A110615

Adjacent sequences: A282665 A282666 A282667 * A282669 A282670 A282671

Keyword

nonn

Author

Emmanuel Vantieghem, Feb 20 2017

Status

approved