A337674 Numbers k whose prime divisors are all less than or equal to the number of divisors of k.

1, 2, 4, 6, 8, 9, 12, 16, 18, 20, 24, 27, 30, 32, 36, 40, 42, 45, 48, 50, 54, 56, 60, 64, 70, 72, 75, 80, 81, 84, 90, 96, 100, 105, 108, 112, 120, 126, 128, 132, 135, 140, 144, 150, 160, 162, 168, 180, 189, 192, 196, 198, 200, 210, 216, 220, 224, 225, 240, 243, 250

Offset: 1

Author

Richard Peterson, Sep 15 2020

Keywords

• nonn

Comments

Density: 33 terms between 1 and 100, 17 between 201 and 300, 11 between 1001 and 1100, and 2 between 1000001 and 1000100.

Examples

			42=a(17) is a term, since 2,3 and 7 are the prime divisors of 42, which has 8 divisors. 156=2^2*3*13 is not a term, since 13 is greater than 12, the number of divisors of 156.
		

Crossrefs

A199768 has "strictly less", while this sequence has "less than or equal to".

The union of A199768 and A036878.

A146982 does not include terms 42, 56, 132, 198, 220, 264, 308, 312, 330, ...

Cf. A000005.

Programs

Mathematica

Select[Range[250], FactorInteger[#][[-1, 1]] <= DivisorSigma[0, #] &] (* Amiram Eldar, Sep 22 2020 *)

PARI

isok(m) = #select(x->(x>numdiv(m)), factor(m)[,1]) == 0; \\ Michel Marcus, Sep 22 2020