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A145293 a(n) is the smallest nonnegative x such that the Euler polynomial x^2 + x + 41 has exactly n distinct prime proper divisors.

%I A145293 #29 Dec 24 2018 03:26:18
%S A145293 0,41,420,2911,38913,707864,6618260,78776990,725005500
%N A145293 a(n) is the smallest nonnegative x such that the Euler polynomial x^2 + x + 41 has exactly n distinct prime proper divisors.
%C A145293 The Euler polynomial gives primes for consecutive x from 0 to 39.
%C A145293 For numbers x for which x^2 + x + 41 is not prime, see A007634.
%C A145293 For composite numbers of the form x^2 + x + 41, see A145292.
%e A145293 a(1)=0 because when x=0 then x^2+x+41=41 (1 distinct prime divisor);
%e A145293 a(2)=41 because when x=41 then x^2+x+41=1763=41*43 (2 distinct prime divisors);
%e A145293 a(3)=420 because when x=420 then x^2+x+41=176861=47*53*71 (3 distinct prime divisors);
%e A145293 a(4)=2911 because when x=2911 then x^2+x+41=8476873=41*47*53*83 (4 distinct prime divisors);
%e A145293 a(5)=38913 because when x=38913 then x^2+x+41=1514260523=43*47*61*71*173 (5 distinct prime divisors);
%e A145293 a(6)=707864 because when x=707864 then x^2+x+41=501072150401=41*43*47*53*71*1607 (6 distinct prime divisors);
%e A145293 a(7)=6618260 because when x=6618260 then x^2+x+41=43801372045901=41*43*47*61*83*131*797 (7 distinct prime divisors);
%e A145293 a(8)=78776990 because when x=78776990 then x^2+x+41=6205814232237131=41*43*61*71*97*131*167*383 (8 distinct prime divisors).
%e A145293 a(9)=725005500: a(9)^2 + a(9) + 41 = 525632975755255541 = 41*43*47*53*61*71*151*397*461. - _Hugo Pfoertner_, Mar 05 2018
%t A145293 a = {}; Do[x = 1; While[Length[FactorInteger[x^2 + x + 41]] < k - 1, x++ ]; AppendTo[a, x]; Print[x], {k, 2, 10}]; a
%Y A145293 Cf. A005846, A007634, A097822, A145292, A145294, A145295.
%Y A145293 Cf. A228122. - _Zak Seidov_, Feb 03 2016
%K A145293 nonn,more
%O A145293 1,2
%A A145293 _Artur Jasinski_, Oct 07 2008
%E A145293 Corrected and edited, a(8) added by _Zak Seidov_, Jan 31 2016
%E A145293 Example for a(8) corrected by _Hugo Pfoertner_, Mar 02 2018
%E A145293 a(9) from _Hugo Pfoertner_, Mar 05 2018