A181845 Triangle read by rows: T(n,k) = max_{c in P(n,n-k+1)} lcm(c) where P(n,m) = A008284(n,m) is the number of partitions of n into m parts.

1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 6, 5, 1, 2, 3, 6, 5, 6, 1, 2, 3, 6, 6, 12, 7, 1, 2, 3, 6, 6, 12, 15, 8, 1, 2, 3, 6, 6, 12, 15, 20, 9, 1, 2, 3, 6, 6, 12, 15, 30, 21, 10, 1, 2, 3, 6, 6, 12, 15, 30, 21, 30, 11, 1, 2, 3, 6, 6, 12, 15, 30, 30, 60, 35, 12

Offset: 1

Author

Peter Luschny, Dec 07 2010

Keywords

• nonn
• tabl

Comments

See A181842 for the definition of 'partition'. T(n,k) is also the triangle read by rows: T(n,k) = max_{c in C(n,n-k+1)} lcm(c) where C(n,m) is the set of all m-tuples of positive integers whose elements sum to n where the C(n,k) = A007318(n-1,k-1) are called compositions of n of size k.

Examples

			[1]   1
[2]   1   2
[3]   1   2   3
[4]   1   2   3   4
[5]   1   2   3   6   5
[6]   1   2   3   6   5   6
[7]   1   2   3   6   6   12   7
[8]   1   2   3   6   6   12   15   8
[9]   1   2   3   6   6   12   15   20   9
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)

Crossrefs

Cf. A181842, A181843, A181844.

Programs

Maple

with(combstruct):
a181845_row := proc(n) local k,L,l,R,part;
R := NULL;
for k from 1 to n do
   L := 0;
   part := iterstructs(Partition(n),size=n-k+1):
# alternatively (but slower)
# part := iterstructs(Composition(n), size=n-k+1):
   while not finished(part) do
      l := nextstruct(part);
      L := max(L,ilcm(op(l)));
   od;
   R := R,L;
od;
R end:

PARI

Row(n)={my(v=vector(n)); forpart(p=n, my(i=#p); v[i]=max(v[i], lcm(Vec(p)))); Vecrev(v)}
{ for(n=1, 10, print(Row(n))) } \\ Andrew Howroyd, Apr 20 2021

Extensions

Terms a(56) and beyond from Andrew Howroyd, Apr 20 2021