A395866 Numbers k such that k-5 and k+5 are prime and gcd(k, sigma(k)) is prime.

18, 162, 648, 3924, 5328, 5652, 22068, 28224, 30708, 48528, 51444, 57168, 60948, 63108, 94608, 116964, 123588, 125712, 131904, 133092, 136242, 139392, 140004, 148068, 164196, 170244, 172872, 173268, 186768, 196164, 207936, 220356, 220788, 223056, 229428, 229842

Offset

1,1

Comments

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

All computed terms are divisible by 18.

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

Links

Table of n, a(n) for n=1..36.

Example

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.
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.

Mathematica

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

Prog

(Python)
from sympy import divisor_sigma, gcd, isprime
def ok(k): return isprime(k-5) and isprime(k+5) and isprime(gcd(k, divisor_sigma(k)))
print([k for k in range(1, 500000) if ok(k)])

Crossrefs

Intersection of A087696 and A392199.

Cf. A087680, A087695, A394757, A395258.

Sequence in context: A002698 A222914 A171642 * A158808 A271899 A128797

Adjacent sequences: A395863 A395864 A395865 * A395867 A395868 A395869

Keyword

nonn

Author

Aied Sulaiman, May 08 2026

Status

approved