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

1,1

Comments

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

Links

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A062090 (a different sequence).

Sequence in context: A308838 A080429 A326581 * A062090 A358975 A345898

Adjacent sequences: A050147 A050148 A050149 * A050151 A050152 A050153

Keyword

easy,nonn,nice

Author

Jason Earls, Jul 04 2001

Extensions

More terms from Jud McCranie, Oct 31 2001

Status

approved