A052215 - OEIS

%I #31 Jul 16 2023 02:38:16

%S 2,14,230,7314,378014,11243154,965009045,65893166030,5702759516090,

%T 605247139068494,78971815814237709,22593106657425552170

%N a(n) = smallest number m such that m and m+1 are the product of exactly n distinct primes.

%C Prime factors may not be repeated in m and m+1. The difference between this sequence and A093548 is that in the latter, prime factors may be repeated. So the present sequence imposes more stringent conditions than A093548, hence a(n) >= A093548(n). - _N. J. A. Sloane_, Nov 21 2015

%C A115186(n) <= A093548(n) <= a(n). - _Zak Seidov_, Jan 16 2015

%C 2^63 < a(12) <= 22593106657425552170. [_Donovan Johnson_, Oct 23 2008]

%C a(12) confirmed to be the upper limit of the range above. - _Bert Dobbelaere_, Jun 27 2019

%e 14 and 15 are both the product of 2 primes.

%e 230 is the 3rd entry because we have (230=2*5*23, 231=3*7*11).

%Y Cf. A093548 (another version), A093549, A093550, A115186, A318896.

%Y Subsequence of A005117.

%K hard,nice,nonn,more

%O 1,1

%A _Erich Friedman_, Jan 29 2000

%E More terms from _Naohiro Nomoto_, Jul 08 2001

%E a(7) from _Farideh Firoozbakht_, Apr 06 2004

%E a(8)-a(10) from _Martin Fuller_, Jan 17 2006

%E a(11) from _Donovan Johnson_, Oct 23 2008

%E a(12) from _Bert Dobbelaere_, Jun 27 2019