login
A337674
Numbers k whose prime divisors are all less than or equal to the number of divisors of k.
0
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.
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
KEYWORD
nonn
AUTHOR
Richard Peterson, Sep 15 2020
STATUS
approved