A345765 Numbers k with property that for p prime, p | k iff (p - 1) | k.

1806, 12642, 88494, 6030842622, 259326232746, 11151028008078, 468349207181898, 479494204347354, 20139015908821614, 20618250786936222, 865977684079329402, 886584783838257546, 36371531080539016782, 37237040415411164286, 38123145705045074478, 1563975836463177721626

Offset

1,1

Comments

All terms are divisible by 1806. A345975 provides the terms divided by the common factor.

1806 is the only squarefree term.

Links

Mees de Vries, Table of n, a(n) for n = 1..126

Mees de Vries, Code for generating large instances

Formula

a(n) = 1806*A345975(n).

Example

The prime divisors of 1806 are 2, 3, 7, 43. 1806 is divisible by each of 1, 2, 6, 42. The remaining even divisors of 1806 are 14, 86, 602, 1806, and none of 15, 87, 603 or 1807 are prime.

Prog

(Python)
from sympy import isprime, divisors, primefactors
def a(n): return all(n % (div + 1) == 0 for div in divisors(n) if isprime(div + 1)) and all(n % (div - 1) == 0 for div in primefactors(n))
(Python) See De Vries link.

Crossrefs

Subsequence of A124240, which only has the requirement p | k implies (p - 1) | k.

Cf. A345975.

Sequence in context: A196788 A252029 A250385 * A035868 A122477 A134155

Adjacent sequences: A345762 A345763 A345764 * A345766 A345767 A345768

Keyword

nonn

Author

Mees de Vries, Jun 26 2021

Status

approved