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A324939 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).

%I A324939 #45 Apr 27 2021 11:30:39
%S A324939 1,2,4,6,8,12,18,30,16,24,36,54,60,90,150,210,32,48,72,108,120,162,
%T A324939 180,270,300,420,450,630,750,1050,1470,2310,64,96,144,216,240,324,360,
%U A324939 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 A324939 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 A324939 All terms sorted give A055932.
%C A324939 All terms first sorted by number of factors give A057335.
%H A324939 Alois P. Heinz, <a href="/A324939/b324939.txt">Rows n = 0..16, flattened</a>
%H A324939 Wikipedia, <a href="https://en.wikipedia.org/wiki/G%C3%B6del_numbering#G%C3%B6del&#39;s_encoding">Gödel's encoding</a>
%e A324939 Triangle T(n,k) begins:
%e A324939    1;
%e A324939    2;
%e A324939    4,  6;
%e A324939    8, 12, 18,  30;
%e A324939   16, 24, 36,  54,  60,  90, 150, 210;
%e A324939   32, 48, 72, 108, 120, 162, 180, 270, 300, 420, 450, 630, 750, 1050, 1470, 2310;
%e A324939   ...
%p A324939 b:= n-> `if`(n=0, [[]], [seq(map(x-> [j, x[]], b(n-j))[], j=1..n)]):
%p A324939 T:= n-> sort(map(x-> mul(ithprime(i)^x[i], i=1..nops(x)), b(n)))[]:
%p A324939 seq(T(n), n=0..7);
%Y A324939 Column k=1 gives A000079.
%Y A324939 Last elements of rows give A002110.
%Y A324939 Row sums give A325054.
%Y A324939 Row lengths give A011782.
%Y A324939 Cf. A000040, A055932, A057335, A087443, A215366.
%K A324939 nonn,tabf
%O A324939 0,2
%A A324939 _Alois P. Heinz_, Sep 04 2019