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A145294
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Smallest x >= 0 such that the Euler polynomial x^2 + x + 41 has a prime divisor of multiplicity n.
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7
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0, 40, 1721, 14144, 2294005, 326924482, 6386359423, 1341160319494, 149759650255065, 1167478867440605, 243422399538851918, 9662500171353620019, 122479951673184550424, 12148820281768361731597, 177497315692809432279207, 11767210525408975519141638
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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