A219209 Maximal product of all parts of a partition of n into distinct divisors of n.

1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 48, 13, 14, 15, 16, 17, 162, 19, 200, 21, 22, 23, 1152, 25, 26, 27, 784, 29, 1350, 31, 32, 33, 34, 35, 15552, 37, 38, 39, 6400, 41, 2058, 43, 44, 45, 46, 47, 73728, 49, 50, 51, 52, 53, 8748, 55, 25088, 57, 58, 59, 864000

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Example

a(0) = 1: the empty product.
a(p) = p for any prime p: [p]-> p.
a(12) = 48: [2,4,6]-> 48.
a(20) = 200: [1,4,5,10]-> 200.
a(24) = 1152: [1,2,3,4,6,8]-> 1152.

Maple

a:= proc(n) local b, l;
      l:= sort([numtheory[divisors](n)[]]);
      b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
            max(b(n, i-1), `if`(l[i]>n, 0, l[i] *b(n-l[i], i-1)))))
          end; forget(b);
      b(n, nops(l))
    end:
seq(a(n), n=0..80);

Mathematica

a[n_] := a[n] = Module[{b, l}, l = Divisors[n]; b[m_, i_] := b[m, i] = If[m == 0, 1, If[i<1, 0, Max[b[m, i-1], If[l[[i]]>m, 0, l[[i]]*b[m-l[[i]], i-1] ]]]]; b[n, Length[l]]]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Feb 16 2017, translated from Maple *)

Crossrefs

The number of distinct products are in A219208.

Cf. A033630, A092976.

Sequence in context: A004851 A066638 A285769 * A223474 A062279 A088599

Adjacent sequences: A219206 A219207 A219208 * A219210 A219211 A219212

Keyword

nonn

Author

Alois P. Heinz, Nov 14 2012

Status

approved