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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. 9
 0, 41, 420, 2911, 38913, 707864, 6618260, 78776990, 725005500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Euler polynomial gives primes for consecutive x from 0 to 39. For numbers x for which x^2 + x + 41 is not prime, see A007634. For composite numbers of the form x^2 + x + 41, see A145292. LINKS EXAMPLE a(1)=0 because when x=0 then x^2+x+41=41 (1 distinct prime divisor); a(2)=41 because when x=41 then x^2+x+41=1763=41*43 (2 distinct prime divisors); a(3)=420 because when x=420 then x^2+x+41=176861=47*53*71 (3 distinct prime divisors); a(4)=2911 because when x=2911 then x^2+x+41=8476873=41*47*53*83 (4 distinct prime divisors); a(5)=38913 because when x=38913 then x^2+x+41=1514260523=43*47*61*71*173 (5 distinct prime divisors); a(6)=707864 because when x=707864 then x^2+x+41=501072150401=41*43*47*53*71*1607 (6 distinct prime divisors); a(7)=6618260 because when x=6618260 then x^2+x+41=43801372045901=41*43*47*61*83*131*797 (7 distinct prime divisors); 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). a(9)=725005500: a(9)^2 + a(9) + 41 = 525632975755255541 = 41*43*47*53*61*71*151*397*461. - Hugo Pfoertner, Mar 05 2018 MATHEMATICA a = {}; Do[x = 1; While[Length[FactorInteger[x^2 + x + 41]] < k - 1, x++ ]; AppendTo[a, x]; Print[x], {k, 2, 10}]; a CROSSREFS Cf. A005846, A007634, A097822, A145292, A145294, A145295. Cf. A228122. - Zak Seidov, Feb 03 2016 Sequence in context: A190421 A178387 A068849 * A196807 A267325 A083761 Adjacent sequences:  A145290 A145291 A145292 * A145294 A145295 A145296 KEYWORD nonn,more AUTHOR Artur Jasinski, Oct 07 2008 EXTENSIONS Corrected and edited, a(8) added by Zak Seidov, Jan 31 2016 Example for a(8) corrected by Hugo Pfoertner, Mar 02 2018 a(9) from Hugo Pfoertner, Mar 05 2018 STATUS approved

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Last modified June 20 06:56 EDT 2021. Contains 345157 sequences. (Running on oeis4.)