A377852 Triangle T(n,k) read by rows in which n-th row lists in increasing order all multiplicative partitions mu of n whose sum is also n (with factors >= 1), encoded as Product_{j in mu} prime(j); n>=1, 1<=k<=A001055(n).
2, 3, 5, 7, 9, 11, 13, 30, 17, 19, 84, 108, 23, 200, 29, 264, 31, 37, 624, 1120, 1440, 41, 43, 1632, 47, 7040, 53, 3648, 12544, 16128, 20736, 59, 61, 8832, 33280, 76800, 67, 71, 22272, 157696, 202752, 73, 174080, 79, 47616, 83, 89, 113664, 778240, 1490944, 1916928, 3440640, 4423680
Offset: 1
Examples
The multiplicative partitions of n=8 whose sum is also n are {[8], [4,2,1,1], [2,2,2,1,1]}, encodings give {prime(8), prime(4)*prime(2)*prime(1)^2, prime(2)^3*prime(1)^2} = {19, 7*3*2^2, 3^3*2^2} => row 8 = [19, 84, 108].
For n=1 the partition [1] gives prime(1) = 2.
Triangle T(n,k) begins:
2 ;
3 ;
5 ;
7, 9 ;
11
13, 30 ;
17 ;
19, 84, 108 ;
23, 200 ;
29, 264 ;
31 ;
37, 624, 1120, 1440 ;
41 ;
43, 1632 ;
47, 7040 ;
53, 3648, 12544, 16128, 20736 ;
59 ;
...
Links
- Alois P. Heinz, Rows n = 1..1000, flattened