A050150 Odd numbers with prime number of divisors.

3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241

Offset: 1

Author

Jason Earls, Jul 04 2001

Keywords

• easy
• nonn
• nice

Comments

Here but not in A062090: [729, 15625, 59049, 117649, 531441]; in A062090 but not here: [1, 6561, 390625]. - Klaus Brockhaus, Nov 01 2001

Examples

			Numbers of the form p^6 for example (such as 3^6 = 729) are here but not in A062090.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A062090 (a different sequence).

Programs

Haskell

a050150 n = a050150_list !! (n-1)
a050150_list = filter ((== 1) . a010051 . (+ 1) . a100995) [1, 3 ..]
-- Reinhard Zumkeller, Aug 16 2013

Mathematica

Select[ Range[1, 250, 2], PrimeQ[ Length[ Divisors[ # ]]] & ]
Select[Range[1,799,2],PrimeQ[DivisorSigma[0,#]]&] (* Harvey P. Dale, Jun 22 2011 *)

PARI

forstep(n=1,1000,2, if(isprime(numdiv(n)),print1(n,",")))

PARI

is(n)=n%2 && isprime(isprimepower(n)+1) \\ Charles R Greathouse IV, Aug 28 2013

Python

from sympy import divisor_count, isprime
def ok(n): return n and n%2 and isprime(divisor_count(n))
print([k for k in range(250) if ok(k)]) # Michael S. Branicky, Jul 05 2022

Formula

Numbers of the form p^e where p is an odd prime and e+1 is a prime.

A010051(A100995(a(n)) + 1) = 1. - Reinhard Zumkeller, Aug 16 2013

a(n) ~ n log n. - Charles R Greathouse IV, Aug 28 2013

Extensions

More terms from Jud McCranie, Oct 31 2001