OFFSET
1,2
COMMENTS
a(n) = lcm(p1,p2,...,pk) for that partition of n for which the LCM is a multiple of n, and which maximizes this value among all such partitions [p1,p2,...,pk] of n.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..100 (terms n = 0..83 from Antti Karttunen)
MAPLE
b:= proc(n, i) option remember; `if`(n=0, {1},
`if`(i<1, {}, {seq(map(x->ilcm(x, `if`(j=0, 1, i)),
b(n-i*j, i-1))[], j=0..n/i)}))
end:
a:= n-> max(select(x-> irem(x, n)=0, b(n$2))[]):
seq(a(n), n=1..50); # Alois P. Heinz, May 26 2013
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, {1}, If[i<1, {}, Union @ Flatten @ Table[ Map[ Function[{x}, LCM[x, If[j==0, 1, i]]], b[n-i*j, i-1]], {j, 0, n/i}]]]; a[n_] := Max[Select[b[n, n], Mod[#, n]==0&]]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Jul 29 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 19 2013
STATUS
approved