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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.

%I A181845 #12 Apr 20 2021 20:18:27
%S A181845 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,
%T A181845 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,
%U A181845 15,30,21,30,11,1,2,3,6,6,12,15,30,30,60,35,12
%N 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.
%C A181845 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.
%H A181845 Andrew Howroyd, <a href="/A181845/b181845.txt">Table of n, a(n) for n = 1..1275</a> (rows 1..50)
%e A181845 [1]   1
%e A181845 [2]   1   2
%e A181845 [3]   1   2   3
%e A181845 [4]   1   2   3   4
%e A181845 [5]   1   2   3   6   5
%e A181845 [6]   1   2   3   6   5   6
%e A181845 [7]   1   2   3   6   6   12   7
%e A181845 [8]   1   2   3   6   6   12   15   8
%e A181845 [9]   1   2   3   6   6   12   15   20   9
%p A181845 with(combstruct):
%p A181845 a181845_row := proc(n) local k,L,l,R,part;
%p A181845 R := NULL;
%p A181845 for k from 1 to n do
%p A181845    L := 0;
%p A181845    part := iterstructs(Partition(n),size=n-k+1):
%p A181845 # alternatively (but slower)
%p A181845 # part := iterstructs(Composition(n), size=n-k+1):
%p A181845    while not finished(part) do
%p A181845       l := nextstruct(part);
%p A181845       L := max(L,ilcm(op(l)));
%p A181845    od;
%p A181845    R := R,L;
%p A181845 od;
%p A181845 R end:
%o A181845 (PARI) Row(n)={my(v=vector(n)); forpart(p=n, my(i=#p); v[i]=max(v[i], lcm(Vec(p)))); Vecrev(v)}
%o A181845 { for(n=1, 10, print(Row(n))) } \\ _Andrew Howroyd_, Apr 20 2021
%Y A181845 Cf. A181842, A181843, A181844.
%K A181845 nonn,tabl
%O A181845 1,3
%A A181845 _Peter Luschny_, Dec 07 2010
%E A181845 Terms a(56) and beyond from _Andrew Howroyd_, Apr 20 2021