A185397 Largest number x such that the greatest prime factor of x^2+2 is A033203(n), the n-th prime not congruent to 5 or 7 mod 8.

22, 140, 707, 21362, 4991, 1306066, 137965, 2294636, 31768298, 1557652, 340064590, 38439662, 105080665, 273502688, 543164542, 9575480365630, 391890109484, 14629598023, 80849485336, 1241646894380

Offset: 1

Author

Charles R Greathouse IV, Feb 21 2011

Keywords

• nonn

Comments

For any prime p, there are finitely many x such that x^2+2 has p as its largest prime factor.

Links

• Filip Najman, Smooth values of some quadratic polynomials, Glasnik Matematicki Series III 45 (2010), pp. 347-355.
• Filip Najman, Home Page (gives all 914 numbers x such that x^2+2 has no prime factor greater than 193)

Crossrefs

Equivalents for other polynomials: A175607 (x^2 - 1), A145606 (x^2 + x), A185389 (x^2 + 1), A185396 (x^2 - 2).