A345765 - OEIS

%I #19 Jul 04 2021 17:20:37

%S 1806,12642,88494,6030842622,259326232746,11151028008078,

%T 468349207181898,479494204347354,20139015908821614,20618250786936222,

%U 865977684079329402,886584783838257546,36371531080539016782,37237040415411164286,38123145705045074478,1563975836463177721626

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

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

%C 1806 is the only squarefree term.

%H Mees de Vries, <a href="/A345765/b345765.txt">Table of n, a(n) for n = 1..126</a>

%H Mees de Vries, <a href="https://github.com/mjdv/saturated-numbers">Code for generating large instances</a>

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

%e 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.

%o (Python)

%o from sympy import isprime, divisors, primefactors

%o 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))

%o (Python) See De Vries link.

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

%Y Cf. A345975.

%K nonn

%O 1,1

%A _Mees de Vries_, Jun 26 2021