A394569 - OEIS

%I #10 Mar 29 2026 20:33:00

%S 4,6,10,12,14,18,22,26,27,30,34,38,42,45,46,54,58,62,63,64,66,74,75,

%T 78,80,82,86,90,94,99,102,105,106,114,117,118,120,122,126,134,138,142,

%U 146,147,150,153,158,160,165,166,171,174,178,180,186,194,195,198,200,202

%N Numbers k such that gcd(k, Omega(k)) is prime.

%C No prime belongs to this sequence since, for any prime k, Omega(k) = 1 and gcd(k, 1) = 1, which is not prime.

%C 2^n is a term if and only if n == 2 (mod 4), since Omega(2^n) = n and gcd(2^n, n) = 2 only in this case.

%e For k = 6: Omega(6) = 2 and gcd(6, 2) = 2, which is prime, so 6 is a term.

%e For k = 8: Omega(8) = 3 and gcd(8, 3) = 1, which is not prime, so 8 is not a term.

%t Select[Range[200], PrimeQ[GCD[#, PrimeOmega[#]]] &] (* _Amiram Eldar_, Mar 25 2026 *)

%o (Python)

%o from sympy import factorint, gcd, isprime

%o def ok(k): return isprime(gcd(k, sum(factorint(k).values())))

%o print([k for k in range(1, 400) if ok(k)])

%Y Cf. A001222, A392199, A394433.

%K nonn,easy

%O 1,1

%A _Aied Sulaiman_, Mar 25 2026