

A097822


Numbers n such that n^2+n+41 (Euler's "prime generating polynomial") has more than 2 prime factors.


4



420, 431, 491, 492, 514, 533, 573, 574, 603, 614, 655, 686, 738, 775, 798, 858, 861, 890, 895, 901, 904, 917, 919, 942, 984, 989, 1025, 1059, 1116, 1130, 1162, 1169, 1188, 1215, 1222, 1224, 1245, 1251, 1253, 1268, 1271, 1318, 1321, 1334, 1365, 1374, 1407
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OFFSET

1,1


COMMENTS

All visible sequence terms give exactly 3 prime factors. The smallest composite of the form p(n)=n^2+n+41 with 4 prime factors occurs for p(1721)=2963603=43*41^3. Smallest n with 4 distinct prime factors: p(2911)=8476873=83*53*47*41, smallest n with 5 prime factors: p(14144)=200066921=47^4*41, smallest n with 5 distinct prime factors: p(38913)=1514260523=173*71*61*47*43.


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..5000
Eric Weisstein's World of Mathematics, PrimeGenerating Polynomial


EXAMPLE

a(1)=420 because 420^2+420+41=176861=71*53*47 is the first n for which p(n)=n^2+n+41 has more than 2 prime factors. For all smaller n p(n) is either prime or semiprime.


MATHEMATICA

Select[Range[1500], PrimeOmega[#^2+#+41]>2&] (* Harvey P. Dale, Dec 26 2017 *)


PROG

(PARI) isok(n) = #factor(n^2+n+41)~ > 2; \\ Michel Marcus, Sep 07 2017


CROSSREFS

Cf. A002837, A007634, A005846, A097823, A145293.
Sequence in context: A187218 A239253 A061118 * A069064 A024410 A200521
Adjacent sequences: A097819 A097820 A097821 * A097823 A097824 A097825


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Aug 26 2004


EXTENSIONS

Corrected a(19) by Hugo Pfoertner, Sep 07 2017


STATUS

approved



