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A345765
Numbers k with property that for p prime, p | k iff (p - 1) | k.
4
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.
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
KEYWORD
nonn
AUTHOR
Mees de Vries, Jun 26 2021
STATUS
approved