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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.
3

%I #13 Mar 08 2023 19:55:46

%S 2,6,354,210,43860,463980,189583590,6958972020,200007607800,

%T 60958204112190,3337686588286050

%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.

%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)=189583590 because 189583590=2*3*5*7*41*97*227, all the seven numbers 2*189583590+1, 3*189583590+1, 5*189583590+1, 7*189583590+1, 41*189583590+1, 97*189583590+1 and 227*189583590+1 are prime numbers and 189583590 is the smallest number m with such property.

%Y Cf. A092023.

%Y Cf. A112723, A112724.

%K more,nonn

%O 1,1

%A _Farideh Firoozbakht_, Feb 19 2004

%E a(10) from _Michael S. Branicky_, Feb 27 2023

%E a(11) from _Michael S. Branicky_, Mar 08 2023