A240549 -id:A240549 - cp's OEIS frontend

A240548 Greatest prime factor of n^5 + 1.

2, 11, 61, 41, 521, 101, 191, 331, 1181, 9091, 13421, 19141, 2411, 101, 1531, 61681, 101, 9041, 2251, 152381, 185641, 224071, 211, 5791, 9161, 1021, 271, 53951, 401, 71261, 21821, 4051, 1151041, 259631, 132631, 6781, 1824841, 2031671, 41011, 20641, 4111, 23201

Offset: 1

T. D. Noe, Apr 07 2014

nonn

			a(2) = 11 because 2^5 + 1 = 33 = 3 * 11.
a(3) = 61 because 3^5 + 1 = 244 = 2^2 * 61.
a(4) = 41 because 4^5 + 1 = 1025 = 5^2 * 41.
a(2272) = 2273 because 2272^5 + 1 = 11^2 * 311 * 491 * 1171 * 1231 * 2273.

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A002561, A014442, A081256, A096172, A240549-A240553.

Table[FactorInteger[n^5 + 1][[-1, 1]], {n, 100}]

A240552 Greatest prime factor of n^9+1.

Original entry on oeis.org

2, 19, 37, 109, 5167, 46441, 117307, 87211, 530713, 52579, 590077, 1801, 937, 132049, 811, 38737, 5653, 465841, 236377, 69481, 613, 5966803, 1117, 7561, 6597973, 102966067, 19927, 102547, 10435069, 120871, 1538083, 18837001, 221401, 745903, 612740917, 55117

Offset: 1

T. D. Noe, Apr 07 2014

nonn

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A014442, A081256, A096172, A240548, A240549, A240550, A240551, A240553.

Table[FactorInteger[n^9 + 1][[-1, 1]], {n, 100}]

a(n) = vecmax(factor(n^9+1)[,1]); \\ Michel Marcus, Dec 17 2017

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

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A240548 Greatest prime factor of n^5 + 1.

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A240552 Greatest prime factor of n^9+1.

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A321069 Greatest prime factor of n^3+2.

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