%I #45 Apr 27 2021 11:30:39
%S 1,2,4,6,8,12,18,30,16,24,36,54,60,90,150,210,32,48,72,108,120,162,
%T 180,270,300,420,450,630,750,1050,1470,2310,64,96,144,216,240,324,360,
%U 486,540,600,810,840,900,1260,1350,1500,1890,2100,2250,2940,3150,3750,4410,4620,5250,6930,7350,10290,11550,16170,25410,30030
%N Triangle T(n,k) read by rows in which n-th row lists in increasing order all compositions [c_1, c_2, ..., c_q] of n encoded as Product_{i=1..q} prime(i)^(c_i); n>=0, 1<=k<=A011782(n).
%C All terms sorted give A055932.
%C All terms first sorted by number of factors give A057335.
%H Alois P. Heinz, <a href="/A324939/b324939.txt">Rows n = 0..16, flattened</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/G%C3%B6del_numbering#G%C3%B6del's_encoding">Gödel's encoding</a>
%e Triangle T(n,k) begins:
%e 1;
%e 2;
%e 4, 6;
%e 8, 12, 18, 30;
%e 16, 24, 36, 54, 60, 90, 150, 210;
%e 32, 48, 72, 108, 120, 162, 180, 270, 300, 420, 450, 630, 750, 1050, 1470, 2310;
%e ...
%p b:= n-> `if`(n=0, [[]], [seq(map(x-> [j, x[]], b(n-j))[], j=1..n)]):
%p T:= n-> sort(map(x-> mul(ithprime(i)^x[i], i=1..nops(x)), b(n)))[]:
%p seq(T(n), n=0..7);
%Y Column k=1 gives A000079.
%Y Last elements of rows give A002110.
%Y Row sums give A325054.
%Y Row lengths give A011782.
%Y Cf. A000040, A055932, A057335, A087443, A215366.
%K nonn,tabf
%O 0,2
%A _Alois P. Heinz_, Sep 04 2019