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

1,2

Comments

Intersection of A061345 and A014076.

A014076 set minus A061346.

Links

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

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

Mathematica

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

Prog

(SageMath)
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)]
(PARI) isok(p) = ((p%2) && !isprime(p) && isprimepower(p)) || (p==1); \\ Michel Marcus, Jul 06 2021
(Python)
from sympy import primepi, integer_nthroot
from oeis_sequences.OEISsequences import bisection
def A244623(n):
    def f(x): return int(n-1+x-sum(primepi(integer_nthroot(x, k)[0])-1 for k in range(2, x.bit_length())))
    return bisection(f, n, n) # Chai Wah Wu, Nov 25 2025

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.

Sequence in context: A075109 A319165 A319152 * A339127 A117580 A280609

Adjacent sequences: A244620 A244621 A244622 * A244624 A244625 A244626

Keyword

nonn

Author

Jani Melik, Jul 02 2014

Status

approved