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 A145294 Smallest x >= 0 such that the Euler polynomial x^2 + x + 41 has a prime divisor of multiplicity n. 7
 0, 40, 1721, 14144, 2294005, 326924482, 6386359423, 1341160319494, 149759650255065, 1167478867440605, 243422399538851918, 9662500171353620019, 122479951673184550424, 12148820281768361731597, 177497315692809432279207, 11767210525408975519141638 (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. 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 LINKS Bert Dobbelaere, Table of n, a(n) for n = 1..100 Bert Dobbelaere, Python program EXAMPLE 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 CROSSREFS Cf. A005846, A007634, A145292, A145293, A145295. Sequence in context: A229584 A140702 A223609 * A147520 A190926 A143314 Adjacent sequences:  A145291 A145292 A145293 * A145295 A145296 A145297 KEYWORD nonn AUTHOR Artur Jasinski, Oct 07 2008 EXTENSIONS Title changed, a(1) and a(6) from Hugo Pfoertner, Mar 08 2018 More terms from Bert Dobbelaere, Jan 22 2019 STATUS approved

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Last modified June 17 19:05 EDT 2019. Contains 324198 sequences. (Running on oeis4.)