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A219209 Maximal product of all parts of a partition of n into distinct divisors of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified April 19 18:35 EDT 2019. Contains 322286 sequences. (Running on oeis4.)