A063806 Numbers with a prime number of proper divisors.

4, 6, 8, 9, 10, 12, 14, 15, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 38, 39, 40, 42, 44, 45, 46, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 102, 104

Offset: 1

Author

Henry Bottomley, Aug 20 2001

Keywords

• nonn

Examples

			15 has three proper divisors {1,3,5} and so is on the list; 16 has four {1,2,4,8} and so is not; 17 has one {1} and so is not; 18 has five {1,2,3,6,9} and so is.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

A subset of A002808. Cf. A009087, A032741.

Programs

PARI

n=0; for (m=1, 10^9, if(isprime(numdiv(m) - 1), write("b063806.txt", n++, " ", m); if (n==1000, break))) \\ Harry J. Smith, Aug 31 2009

PARI

is(n)=isprime(numdiv(n)-1) \\ Charles R Greathouse IV, Sep 18 2015