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A244623
Odd prime powers that are not primes.
4
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
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
(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)]
(PARI) isok(p) = ((p%2) && !isprime(p) && isprimepower(p)) || (p==1); \\ Michel Marcus, Jul 06 2021
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
KEYWORD
nonn
AUTHOR
Jani Melik, Jul 02 2014
STATUS
approved