A096172 -id:A096172 - cp's OEIS frontend

A240554 Square array of the greatest prime factor of n^k + 1, read by antidiagonals.

1, 2, 1, 3, 2, 1, 2, 5, 2, 1, 5, 5, 3, 2, 1, 3, 17, 7, 17, 2, 1, 7, 13, 13, 41, 11, 2, 1, 2, 37, 7, 257, 61, 13, 2, 1, 3, 5, 31, 313, 41, 73, 43, 2, 1, 5, 13, 43, 1297, 521, 241, 547, 257, 2, 1, 11, 41, 19, 1201, 101, 601, 113, 193, 19, 2, 1, 3, 101, 73, 241

Offset: 1

T. D. Noe, Apr 07 2014

T. D. Noe, Rows n = 1..60 of triangle, flattened

Cf. A003992 (n^k), A014442 (k=2), A081256 (k=3), A096172 (k=4).

Cf. A240548-A240553 (k=5 to 10).

Table[FactorInteger[(n-k)^k + 1][[-1,1]], {n, 12}, {k, n}]

A321069 Greatest prime factor of n^3+2.

Original entry on oeis.org

3, 5, 29, 11, 127, 109, 23, 257, 43, 167, 43, 173, 733, 1373, 307, 683, 983, 2917, 2287, 4001, 157, 71, 283, 223, 5209, 47, 127, 3659, 24391, 587, 9931, 113, 433, 6551, 809, 569, 307, 27437, 433, 10667, 439, 239, 1559, 223, 91127, 16223, 4153, 457, 39217, 62501

Offset: 1

Charles R Greathouse IV, Oct 27 2018

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
D. R. Heath-Brown, The largest prime factor of x^3+2, Proceedings of the London Mathematical Society, 82:3 (2000), pp. 554-596.
Christopher Hooley, On the greatest prime factor of a cubic polynomial, Journal für die reine und angewandte Mathematik, 303 (1978), pp. 21-50.
A. J. Irving, The largest prime factor of x^3+2, arXiv:1412.0024 [math.NT], 2014.

Greatest prime factors of polynomials: A006530 (n), A076565 (2n+1), A076566 (3n+3), A076567 (4n+6), A164314 (n^2-2), A076605 (n^2-1), A014442 (n^2+1), A069902 (n^2+n), A074399 (n^2+n), A199423 (2n^2+n), A089619 (2n^2+2n+1), A037464 (4n^2-1), A253254 (9n^2-7n), A093074 (n^3-n), A081257 (n^3-1), A081256 (n^3+1), A321069(n^3+2), A281793 (n^3+n^2+n+1), A281793 (n^4-1), A096172 (n^4+1), A190136 (n^4 + 6n^3 + 11n^2 + 6n), A140538 (2n^4+1), A240548 (n^5+1), A281794 (n^5+n^3+n^2+1), A240549 (n^6+1), A240550 (n^7+1), A240551 (n^8+1), A240552 (n^9+1), A240553 (n^10+1).

[Maximum(PrimeDivisors(n^3 + 2)): n in [1..60]]; // Vincenzo Librandi, Oct 27 2018

Table[FactorInteger[n^3 + 2] [[-1, 1]], {n, 80}] (* Vincenzo Librandi, Oct 27 2018 *)

a(n) = vecmax(factor(n^3+2)[,1]); \\ Michel Marcus, Oct 27 2018

cp's OEIS Frontend

A240554 Square array of the greatest prime factor of n^k + 1, read by antidiagonals.

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