A394815 - OEIS

%I #13 May 06 2026 12:08:44

%S 5652,6948,16452,20772,27792,44532,65700,67428,126612,143568,180288,

%T 194868,195732,212868,216900,218628,236772,276372,299700,328788,

%U 369828,377172,390672,400068,402768,425988,437652,441108,463248,483408,491328,530532,536868,539712

%N Numbers k in A014574 (averages of twin prime pairs) such that gcd(k, sigma(k)) = 2.

%C Conjecture: every term is divisible by 36.

%C Conjecturally, A394757 is the disjoint union of this sequence and A394399.

%e For k = 5652: k-1 = 5651 and k+1 = 5653 are prime; also sigma(5652) = 14378 and gcd(5652, 14378) = 2, so 5652 is a term.

%e For k = 18: k-1 = 17 and k+1 = 19 are prime; also sigma(18) = 39 and gcd(18, 39) = 3, so 18 is not a term.

%t q[k_]:=PrimeQ[k-1]&&PrimeQ[k+1]&&GCD[k,DivisorSigma[1,k]]==2;Select[Range[539712],q] (* _James C. McMahon_, May 06 2026 *)

%o (Python)

%o from sympy import divisor_sigma, gcd, isprime

%o def ok(k):

%o     return isprime(k-1) and isprime(k+1) and gcd(k, divisor_sigma(k)) == 2

%o print([k for k in range(1, 600000) if ok(k)])

%Y Subsequence of A394757.

%Y Cf. A014574, A392199, A394399.

%K nonn

%O 1,1

%A _Aied Sulaiman_, May 01 2026