A199768 Numbers whose greatest prime factor is less than their number of divisors.

4, 6, 8, 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, 252

Offset: 1

Author

Franklin T. Adams-Watters, Nov 10 2011

Keywords

• nonn
• easy

Comments

The greatest prime factor equals the number of divisors only for 1 (as defined in A006530) and numbers of the form p^(p-1) for p a prime.

Examples

			4 has 2 as its greatest prime factor, and it has 3 factors (1, 2, 4), so it is in the sequence.
10 has 5 as its greatest prime factor, but it has only 4 factors (1, 2, 5, 10), so it is not in the sequence.
		

Links

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

Crossrefs

Cf. A006530 (greatest prime factor), A000005 (number of divisors), A036878 (p^(p-1)).

Programs

Mathematica

Select[Range[300],FactorInteger[#][[-1,1]]Harvey P. Dale, Nov 19 2011 *)