A395866 - OEIS

%I #7 May 12 2026 23:10:11

%S 18,162,648,3924,5328,5652,22068,28224,30708,48528,51444,57168,60948,

%T 63108,94608,116964,123588,125712,131904,133092,136242,139392,140004,

%U 148068,164196,170244,172872,173268,186768,196164,207936,220356,220788,223056,229428,229842

%N Numbers k such that k-5 and k+5 are prime and gcd(k, sigma(k)) is prime.

%C k is the midpoint of a prime pair (k-5, k+5) differing by 10; this sequence is a subsequence of A087696.

%C All computed terms are divisible by 18.

%C Most computed terms satisfy gcd(k, sigma(k)) = 2, though other prime values also occur.

%e For k = 3924: 3924-5 = 3919 and 3924+5 = 3929 are prime. Also, sigma(3924) = 10010 and gcd(3924, 10010) = 2, which is prime, so 3924 is a term.

%e For k = 12: 12-5 = 7 and 12+5 = 17 are prime, but sigma(12) = 28 and gcd(12, 28) = 4, which is not prime, so 12 is not a term.

%t Select[Range[230000], And @@ PrimeQ[{# - 5, # + 5, GCD[#, DivisorSigma[1, #]]}] &] (* _Amiram Eldar_, May 08 2026 *)

%o (Python)

%o from sympy import divisor_sigma, gcd, isprime

%o def ok(k): return isprime(k-5) and isprime(k+5) and isprime(gcd(k, divisor_sigma(k)))

%o print([k for k in range(1, 500000) if ok(k)])

%Y Intersection of A087696 and A392199.

%Y Cf. A087680, A087695, A394757, A395258.

%K nonn

%O 1,1

%A _Aied Sulaiman_, May 08 2026