A394757 Numbers k in A014574 (averages of twin prime pairs) such that gcd(k, sigma(k)) is prime.

18, 72, 1152, 4050, 5652, 6948, 15138, 16452, 20772, 20808, 27792, 44532, 46818, 65700, 67428, 126612, 143568, 176418, 180288, 194868, 195732, 206082, 212868, 216900, 218628, 236772, 276372, 281250, 299700, 328788, 362952, 369828, 377172, 388962, 390672, 400068, 402768

Offset

1,1

Comments

Conjecture: all terms are divisible by 18.

Conjecture: gcd(k, sigma(k)) is in {2,3}.

Links

Table of n, a(n) for n=1..37.

Example

For k = 18: sigma(18) = 39 and gcd(18, 39) = 3, which is prime, so 18 is a term.
For k = 12: sigma(12) = 28 and gcd(12, 28) = 4, which is not prime, so 12 is not a term.

Mathematica

Select[Array[Prime[#] + 1 &, 35000], PrimeQ[# + 1] && PrimeQ[GCD[#, DivisorSigma[1, #]]] &] (* Amiram Eldar, Mar 31 2026 *)

Prog

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

Crossrefs

Intersection of A014574 and A392199.

Sequence in context: A052619 A110753 A154670 * A394399 A041626 A039608

Adjacent sequences: A394754 A394755 A394756 * A394758 A394759 A394760

Keyword

nonn

Author

Aied Sulaiman, Mar 31 2026

Status

approved