A362779 Triangular array read by rows: T(n,k) is the greatest prime factor of n!*k + 1, n >= 1, 1 <= k <= n.

2, 3, 5, 7, 13, 19, 5, 7, 73, 97, 11, 241, 19, 37, 601, 103, 131, 2161, 67, 277, 149, 71, 593, 15121, 20161, 79, 30241, 35281, 661, 7331, 1657, 161281, 449, 241921, 282241, 6863, 269, 2477, 1088641, 1451521, 78887, 2177281, 5281, 2903041, 192113, 329891, 29383, 10886401, 62297, 18144001, 2243, 251501, 29030401, 32659201, 843907

Offset: 1

Author

Joe B. Stephen, May 03 2023

Keywords

• tabl
• nonn

Comments

The primes in each row are distinct because n!*k + 1 are coprime for 1 <= k <= n, and hence this array gives a simple proof that there are infinitely many prime numbers.

Examples

			Triangle T(n,k) begins:
  n\k   1    2    3    4    5    6 ...
  1     2
  2     3    5
  3     7   13   19
  4     5    7   73   97
  5    11  241   19   37  601
  6   103  131 2161   67  277  149
  ...
		

Crossrefs

Cf. A362777, A362778.

Cf. A002583 (1st column).

Formula

T(n,k) = A006530(A362777(n,k))