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

1,2

Comments

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

Links

Table of n, a(n) for n=1..61.

Example

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.

Mathematica

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

Prog

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

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.

Sequence in context: A354360 A333426 A118363 * A324521 A146982 A352488

Adjacent sequences: A337671 A337672 A337673 * A337675 A337676 A337677

Keyword

nonn

Author

Richard Peterson, Sep 15 2020

Status

approved