A332768 a(n) is the greatest prime factor of A180045(n).

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

Offset: 1

Author

Rémy Sigrist, Feb 23 2020

Keywords

• nonn
• look

Comments

Corvaja and Zannier showed that a(n) tends to infinity as n tends to infinity.

Examples

			The first terms, alongside A180045(n), are:
  n   a(n)  A180045(n)
  --  ----  --------------
   1     7   28 =  7 * 2^2
   2     5   45 =  5 * 3^2
   3    13   65 = 13 * 5
   4    11   66 = 11 * 3 * 2
   5    13   91 = 13 * 7
   6     3   96 =  3 * 2^5
   7    13  117 = 13 * 3^2
   8     5  120 =  5 * 3 * 2^3
   9     7  126 =  7 * 3^2 * 2
  10    19  133 = 19 * 7
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• P. Corvaja and U. Zannier, On the greatest prime factor of (ab+1)(ac+1), arXiv:math/0205136 [math.NT], 2002.
• Rémy Sigrist, PARI program for A332768

Crossrefs

Cf. A006530, A180045, A260234.

Programs

PARI

See Links section.

Formula

a(n) = A006530(A180045(n)).