A244623 Odd prime powers that are not primes.

1, 9, 25, 27, 49, 81, 121, 125, 169, 243, 289, 343, 361, 529, 625, 729, 841, 961, 1331, 1369, 1681, 1849, 2187, 2197, 2209, 2401, 2809, 3125, 3481, 3721, 4489, 4913, 5041, 5329, 6241, 6561, 6859, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12167, 12769, 14641, 15625, 16129, 16807, 17161, 18769, 19321, 19683

Offset: 1

Author

Jani Melik, Jul 02 2014

Keywords

• nonn

Comments

Intersection of A061345 and A014076.

A014076 set minus A061346.

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A005408 and A025475.

Cf. A061345 (odd prime powers), A061346 (odd neither prime nor prime power), A062739 (odd powerful), A075109 (perfect powers), A136141.

Programs

Mathematica

Join[{1},Select[Range[1,20001,2],PrimePowerQ[#]&&(!PrimeQ[#])&]] (* Harvey P. Dale, Dec 11 2018 *)

PARI

isok(p) = ((p%2) && !isprime(p) && isprimepower(p)) || (p==1); \\ Michel Marcus, Jul 06 2021

Sage

def isA244623(n) :
   return(n % 2 == 1 and is_prime_power(n) == 1 and is_prime(n) == 0)
[n for n in (1..20000) if isA244623(n)]

Formula

a(n) = A079290(n) at least in the range n=3..94, and perhaps beyond. - R. J. Mathar, Aug 20 2014

Sum_{n>=1} 1/a(n) = 1/2 + Sum_{p prime} 1/(p*(p-1)) = 1/2 + A136141. - Amiram Eldar, Dec 21 2020