A394399 Numbers k in A014574 (averages of twin prime pairs) such that gcd(k, sigma(k)) = 3.

18, 72, 1152, 4050, 15138, 20808, 46818, 176418, 206082, 281250, 362952, 388962, 472392, 538722, 734472, 1080450, 1152162, 1566450, 1685448, 1808802, 2268450, 2544768, 4339458, 4464072, 4536072, 6118002, 6329682, 7746048, 9305298, 14612418, 14709888, 16623378, 18471042, 19244808

Offset

1,1

Comments

Conjecture: all terms are of the form 2*m^2 (twice a perfect square; A001105).

Links

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

Example

For k = 18: sigma(18) = 39 and gcd(18, 39) = 3, so 18 is a term; moreover 18 = 2*3^2.
For k = 5652: sigma(5652) = 14378 and gcd(5652, 14378) = 2, so 5652 is not a term.

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)) == 3
print([k for k in range(1, 20000000) if ok(k)])

Crossrefs

Conjectural intersection of A014574, A392199 and A001105.

Subsequence of A394757.

Sequence in context: A110753 A154670 A394757 * A041626 A039608 A211619

Adjacent sequences: A394396 A394397 A394398 * A394400 A394401 A394402

Keyword

nonn

Author

Aied Sulaiman, Apr 24 2026

Status

approved