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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

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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

LINKS

Table of n, a(n) for n=1..32.

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

Adjacent sequences: A071849 A071850 A071851 * A071853 A071854 A071855

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

URL: https://oeis.org/A071852

⇱ A071852 - OEIS