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A071852
Smallest k such that 2^k + 1 has exactly n distinct prime factors.
1
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
1,2
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
FORMULA
a(n) = min (k : A046799(k) = n ).
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 *)
PROG
(PARI) for(n=1, 10, s=1; while(abs(omega(2^s+1)-n)>0, s++); print1(s, ", "))
CROSSREFS
Cf. A046799.
Sequence in context: A296692 A102884 A356873 * A275809 A227793 A022139
KEYWORD
nonn,more
AUTHOR
Benoit Cloitre, Jun 09 2002
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
STATUS
approved