A190136 -id:A190136 - cp's OEIS frontend

A093074 Greatest prime factor of n and its direct neighbors.

2, 3, 3, 5, 5, 7, 7, 7, 5, 11, 11, 13, 13, 13, 7, 17, 17, 19, 19, 19, 11, 23, 23, 23, 13, 13, 13, 29, 29, 31, 31, 31, 17, 17, 17, 37, 37, 37, 19, 41, 41, 43, 43, 43, 23, 47, 47, 47, 7, 17, 17, 53, 53, 53, 11, 19, 29, 59, 59, 61, 61, 61, 31, 13, 13, 67, 67, 67, 23, 71, 71, 73

Offset: 1

Reinhard Zumkeller, Mar 18 2004

nonn

a(n) = A006530(n + A093075(n));
a(n) = max{A006530(n-1), A006530(n), A006530(n+1)}, n>1;
a(n) = A006530(A007531(n+1)), n>1;
for all primes p>2: a(p)=a(p-1)=p and if p is not the lesser member of a twin prime pair, then also a(p+1)=p;
(n,n+2) is a twin prime pair iff a(n-1)=a(n)=n and a(n+1)=a(n+2)=a(n+3)=n+2.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A074399, A190136.

a093074 1 = 2
a093074 n = maximum $ map a006530 [n-1..n+1]
-- Reinhard Zumkeller, Jul 04 2012

a(n)=my(p=precprime(n+1));if(p>n-2,p,vecmax(apply(n->vecmax(factor(n)[,1]),[n-1,n,n+1]))) \\ Charles R Greathouse IV, Feb 19 2013

a(n) > 47 if n > 212381. - Charles R Greathouse IV, Feb 19 2013

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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A093074 Greatest prime factor of n and its direct neighbors.

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