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A145294 Smallest x >= 0 such that the Euler polynomial x^2 + x + 41 has a prime divisor of multiplicity n.

%I A145294 #35 Jan 23 2019 16:18:56
%S A145294 0,40,1721,14144,2294005,326924482,6386359423,1341160319494,
%T A145294 149759650255065,1167478867440605,243422399538851918,
%U A145294 9662500171353620019,122479951673184550424,12148820281768361731597,177497315692809432279207,11767210525408975519141638
%N A145294 Smallest x >= 0 such that the Euler polynomial x^2 + x + 41 has a prime divisor of multiplicity n.
%C A145294 The Euler polynomial gives primes for consecutive x from 0 to 39.
%C A145294 For numbers x for which x^2 + x + 41 is not prime, see A007634.
%C A145294 For composite numbers of the form x^2 + x + 41, see A145292.
%C A145294 For the smallest x such that polynomial x^2 + x + 41 has exactly n distinct prime divisors, see A145293.
%C A145294 Sequence interpreted as a(n)^2 + a(n) + 41 having a prime divisor with multiplicity that is exactly n. - _Bert Dobbelaere_, Jan 22 2019
%H A145294 Bert Dobbelaere, <a href="/A145294/b145294.txt">Table of n, a(n) for n = 1..100</a>
%H A145294 Bert Dobbelaere, <a href="/A145294/a145294_1.py.txt">Python program</a>
%e A145294 a(2)=40 because when x=40 then x^2 + x + 41 = 1681 = 41^2;
%e A145294 a(3)=1721 because when x=1721 then x^2 + x + 41 = 2963603 = 43*41^3;
%e A145294 a(4)=14144 because when x=14144 then x^2 + x + 41 = 200066921 = 41*47^4;
%e A145294 a(5)=2294005 because when x=2294005 then x^2 + x + 41 = 5262461234071 = 35797*43^5.
%e A145294 a(6)=326924482: a(6)^2 + a(6) + 41 = 106879617257892847 = 9915343 * 47^6. - _Hugo Pfoertner_, Mar 08 2018
%Y A145294 Cf. A005846, A007634, A145292, A145293, A145295.
%K A145294 nonn
%O A145294 1,2
%A A145294 _Artur Jasinski_, Oct 07 2008
%E A145294 Title changed, a(1) and a(6) from _Hugo Pfoertner_, Mar 08 2018
%E A145294 More terms from _Bert Dobbelaere_, Jan 22 2019