A079290 -id:A079290 - cp's OEIS frontend

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

Jani Melik, Jul 02 2014

nonn

Intersection of A061345 and A014076.

A014076 set minus A061346.

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

Intersection of A005408 and A025475.

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

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

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

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)]

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

A073078 Least k such that n divides C(2k,k).

Original entry on oeis.org

1, 1, 2, 3, 3, 2, 4, 7, 5, 3, 6, 5, 7, 4, 8, 15, 9, 5, 10, 3, 5, 6, 12, 7, 13, 7, 14, 5, 15, 8, 16, 31, 6, 9, 4, 5, 19, 10, 7, 13, 21, 5, 22, 6, 8, 12, 24, 15, 25, 13, 11, 7, 27, 14, 8, 11, 11, 15, 30, 14, 31, 16, 5, 63, 8, 6, 34, 9, 14, 4, 36, 14, 37, 19, 14, 10, 6, 7, 40, 15, 41, 21

Offset: 1

Benoit Cloitre, Aug 17 2002

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000984, A111869.

A073078 := proc(n)
    for k from 1 do
        if modp(binomial(2*k,k),n) = 0 then
            return k;
        end if;
    end do:
end proc: # R. J. Mathar, Aug 20 2014

lk[n_]:=Module[{k=1},While[!Divisible[Binomial[2k,k],n],k++];k]; Array[lk,90] (* Harvey P. Dale, Oct 09 2012 *)

a(n)=if(n<0,0,s=1; while(binomial(2*s,s)%n>0,s++); s)

a(2^k)=2^k-1, if n is an odd prime a(n)=(n+1)/2 (but there are also some composites satisfying this property, see A079290).

cp's OEIS Frontend

A244623 Odd prime powers that are not primes.

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