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

0, 41, 420, 2911, 38913, 707864, 6618260, 78776990, 725005500

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

Table of n, a(n) for n=1..9.

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