A071852 Smallest k such that 2^k + 1 has exactly n distinct prime factors.

1, 5, 14, 18, 30, 42, 99, 114, 78, 90, 175, 150, 324, 210, 315, 234, 270, 585, 405, 765, 390, 450, 510, 1150, 690, 630, 930, 858, 810, 1155, 966, 1386

Offset: 1

Author

Benoit Cloitre, Jun 09 2002

Keywords

• nonn
• more

Comments

a(33) > 1500; a(34) = 1365; a(35) = 1350; a(38) = 1170; a(41) = 1530. - Max Alekseyev, Oct 14 2012

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

Crossrefs

Cf. A046799.

Programs

Mathematica

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

PARI

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

Formula

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

Extensions

175 and 150 from Erich Friedman, Aug 08 2005

a(13)-a(23) from Donovan Johnson, Apr 22 2008

a(24)-a(32) from Max Alekseyev, Oct 14 2012