A071852 - OEIS

%I #29 Sep 03 2022 18:46:32

%S 1,5,14,18,30,42,99,114,78,90,175,150,324,210,315,234,270,585,405,765,

%T 390,450,510,1150,690,630,930,858,810,1155,966,1386

%N Smallest k such that 2^k + 1 has exactly n distinct prime factors.

%C a(33) > 1500; a(34) = 1365; a(35) = 1350; a(38) = 1170; a(41) = 1530. - _Max Alekseyev_, Oct 14 2012

%C a(33) <= 1782; a(36) <= 1710; a(42) <= 2142; a(43) <= 2394; a(44) <= 1890; a(45) <= 2310; a(46) <= 2070. - _Jon E. Schoenfield_, Sep 03 2022

%F a(n) = min (k : A046799(k) = n ).

%t For[n = 1, n < 15, n++, k := 1; While[Not[Length[FactorInteger[2^k + 1]] == n], k++ ]; Print[k]] (* _Stefan Steinerberger_, Apr 09 2006 *)

%o (PARI) for(n=1,10,s=1; while(abs(omega(2^s+1)-n)>0,s++); print1(s,","))

%Y Cf. A046799.

%K nonn,more

%O 1,2

%A _Benoit Cloitre_, Jun 09 2002

%E 175 and 150 from _Erich Friedman_, Aug 08 2005

%E a(13)-a(23) from _Donovan Johnson_, Apr 22 2008

%E a(24)-a(32) from _Max Alekseyev_, Oct 14 2012