OFFSET
0,2
COMMENTS
Integer m > 0 is listed in row n if the index of the largest prime factor of m (or 0 for empty prime factor set) plus the cardinality of the other prime factors of m (counted with multiplicity) equals n.
Row n+k-1 contains prime(n)^k (for all n, k >= 1).
LINKS
EXAMPLE
Triangle T(n,k) begins:
1;
2;
3, 4;
5, 6, 8, 9;
7, 10, 12, 15, 16, 18, 25, 27;
11, 14, 20, 21, 24, 30, 32, 35, 36, 45, 49, 50, 54, 75, 81, 125;
...
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [1], sort([seq(map(x-> x*
ithprime(j), b(n-`if`(i=0, j, 1), j))[], j=1..`if`(i=0, n, i))]))
end:
T:= n-> b(n, 0)[]:
seq(T(n), n=0..7);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, {1}, Sort[Flatten[Table[#*
Prime[j]& /@ b[n-If[i == 0, j, 1], j], {j, 1, If[i == 0, n, i]}]]]];
T[n_] := b[n, 0];
T /@ Range[0, 7] // Flatten (* Jean-François Alcover, Mar 30 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Mar 04 2020
STATUS
approved