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

1,1

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.

Links

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

Example

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.

Mathematica

Select[Range[300], FactorInteger[#][[-1, 1]]<DivisorSigma[0, #]&] (* Harvey P. Dale, Nov 19 2011 *)

Crossrefs

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

Sequence in context: A231569 A337812 A100390 * A157932 A097619 A113709

Adjacent sequences: A199765 A199766 A199767 * A199769 A199770 A199771

Keyword

nonn,easy

Author

Franklin T. Adams-Watters, Nov 10 2011

Status

approved