%I #7 Jan 01 2021 07:21:20
%S 1,2,2,6,2,3,24,8,3,8,120,8,3,8,5,720,48,18,8,5,36,5040,48,18,8,5,36,
%T 7,40320,384,18,64,5,36,7,64,362880,384,162,64,5,36,7,64,27,3628800,
%U 3840,162,64,50,36,7,64,27,100,39916800,3840,162,64,50,36,7,64,27,100,11
%N T(n, k) = Product(divisors(k) union {k*j : j = 2..floor(n/k)}). Triangle read by rows.
%C For the connection with paths in the divisor graph of {1,...,n} see the comment in A339492.
%e The triangle starts:
%e [1] 1;
%e [2] 2, 2;
%e [3] 6, 2, 3;
%e [4] 24, 8, 3, 8;
%e [5] 120, 8, 3, 8, 5;
%e [6] 720, 48, 18, 8, 5, 36;
%e [7] 5040, 48, 18, 8, 5, 36, 7;
%e [8] 40320, 384, 18, 64, 5, 36, 7, 64;
%e [9] 362880, 384, 162, 64, 5, 36, 7, 64, 27;
%e [10] 3628800, 3840, 162, 64, 50, 36, 7, 64, 27, 100;
%p t := (n, k) -> NumberTheory:-Divisors(k) union {seq(k*j, j=2..n/k)}:
%p T := (n, k) -> mul(j, j = t(n, k)):
%p for n from 1 to 10 do seq(T(n, k), k=1..n) od;
%Y T(n, 1) = A000142(n), T(n, n) = A007955(n).
%Y Cf. A339491, A339492, A339496.
%K nonn,tabl
%O 1,2
%A _Peter Luschny_, Dec 31 2020