|
%I #21 Mar 25 2023 22:57:28
%S 2,6,30,420,32550,410970,55137810,1350063330,30644204010,
%T 9396949341780,6805591029957720
%N a(n) is the smallest number m such that m has n distinct prime divisors and if p is a prime divisor of m then p*m - 1 is prime.
%C 2004 has this property, i.e., 2004 = 2^2*3*167, the three numbers 2*2004-1,3*2004-1 and 167*2004-1 are primes. But 2004 is not in the sequence because 2004 is not the smallest number with such property.
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_334.htm">Puzzle 334. Farideh & the 2004 year</a>, The Prime Puzzles & Problems connection.
%e a(7) = 55137810 because 55137810 = 2*3*5*7*13*19*1063 and all the seven numbers 2*55137810-1, 3*55137810-1, 5*55137810-1, 7*55137810-1, 13*55137810-1, 19*55137810-1 and 1063*55137810-1 are prime numbers and 55137810 is the smallest number m with such property.
%Y Cf. A092024.
%Y Cf. A112723, A112724.
%K more,nonn
%O 1,1
%A _Farideh Firoozbakht_, Feb 18 2004
%E a(10) from _Michael S. Branicky_, Feb 25 2023
%E a(11) from _Michael S. Branicky_, Mar 20 2023
|
