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%I #12 Jun 25 2023 01:03:19
%S 2,3,5,7,13,19,5,7,73,97,11,241,19,37,601,103,131,2161,67,277,149,71,
%T 593,15121,20161,79,30241,35281,661,7331,1657,161281,449,241921,
%U 282241,6863,269,2477,1088641,1451521,78887,2177281,5281,2903041,192113,329891,29383,10886401,62297,18144001,2243,251501,29030401,32659201,843907
%N Triangular array read by rows: T(n,k) is the greatest prime factor of n!*k + 1, n >= 1, 1 <= k <= n.
%C 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.
%F T(n,k) = A006530(A362777(n,k))
%e Triangle T(n,k) begins:
%e n\k 1 2 3 4 5 6 ...
%e 1 2
%e 2 3 5
%e 3 7 13 19
%e 4 5 7 73 97
%e 5 11 241 19 37 601
%e 6 103 131 2161 67 277 149
%e ...
%Y Cf. A362777, A362778.
%Y Cf. A002583 (1st column).
%K tabl,nonn
%O 1,1
%A _Joe B. Stephen_, May 03 2023
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