A394815 Numbers k in A014574 (averages of twin prime pairs) such that gcd(k, sigma(k)) = 2.

5652, 6948, 16452, 20772, 27792, 44532, 65700, 67428, 126612, 143568, 180288, 194868, 195732, 212868, 216900, 218628, 236772, 276372, 299700, 328788, 369828, 377172, 390672, 400068, 402768, 425988, 437652, 441108, 463248, 483408, 491328, 530532, 536868, 539712

Offset

1,1

Comments

Conjecture: every term is divisible by 36.

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

Links

Table of n, a(n) for n=1..34.

Example

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.
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.

Mathematica

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

Prog

(Python)
from sympy import divisor_sigma, gcd, isprime
def ok(k):
    return isprime(k-1) and isprime(k+1) and gcd(k, divisor_sigma(k)) == 2
print([k for k in range(1, 600000) if ok(k)])

Crossrefs

Subsequence of A394757.

Cf. A014574, A392199, A394399.

Sequence in context: A359055 A184080 A234401 * A203726 A262660 A255147

Adjacent sequences: A394812 A394813 A394814 * A394816 A394817 A394818

Keyword

nonn

Author

Aied Sulaiman, May 01 2026

Status

approved