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

0, 40, 1721, 14144, 2294005, 326924482, 6386359423, 1341160319494, 149759650255065, 1167478867440605, 243422399538851918, 9662500171353620019, 122479951673184550424, 12148820281768361731597, 177497315692809432279207, 11767210525408975519141638

Offset: 1

Author

Artur Jasinski, Oct 07 2008

Keywords

• nonn

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.

For the smallest x such that polynomial x^2 + x + 41 has exactly n distinct prime divisors, see A145293.

Sequence interpreted as a(n)^2 + a(n) + 41 having a prime divisor with multiplicity that is exactly n. - Bert Dobbelaere, Jan 22 2019

Examples

			a(2)=40 because when x=40 then x^2 + x + 41 = 1681 = 41^2;
a(3)=1721 because when x=1721 then x^2 + x + 41 = 2963603 = 43*41^3;
a(4)=14144 because when x=14144 then x^2 + x + 41 = 200066921 = 41*47^4;
a(5)=2294005 because when x=2294005 then x^2 + x + 41 = 5262461234071 = 35797*43^5.
a(6)=326924482: a(6)^2 + a(6) + 41 = 106879617257892847 = 9915343 * 47^6. - _Hugo Pfoertner_, Mar 08 2018
		

Links

• Bert Dobbelaere, Table of n, a(n) for n = 1..100
• Bert Dobbelaere, Python program

Crossrefs

Cf. A005846, A007634, A145292, A145293, A145295.

Extensions

Title changed, a(1) and a(6) from Hugo Pfoertner, Mar 08 2018

More terms from Bert Dobbelaere, Jan 22 2019