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User: Mees de Vries

Mees de Vries has authored 1 sequences.

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

Mees de Vries, Jun 26 2021

nonn

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

1806 is the only squarefree term.

			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.

Mees de Vries, Table of n, a(n) for n = 1..126
Mees de Vries, Code for generating large instances

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

Cf. A345975.

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.
```

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

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User: Mees de Vries

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

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