The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A266871 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A266871

Number of partitions of n that maximize the product of multiplicities of parts.
(history; published version)

#18 by Bruno Berselli at Wed Dec 21 03:16:31 EST 2016

STATUS

reviewed

approved

#17 by Joerg Arndt at Wed Dec 21 03:10:10 EST 2016

STATUS

proposed

reviewed

#16 by Jean-François Alcover at Wed Dec 21 03:06:30 EST 2016

STATUS

editing

proposed

#15 by Jean-François Alcover at Wed Dec 21 03:06:20 EST 2016

MATHEMATICA

b[n_, i_] := b[n, i] = Module[{r, l, j}, If[n == 0 || i == 1, {Max[1, n], 1}, r = b[n, i - 1]; For[j = 1, j <= Quotient[n, i], j++, l = Function[w, {w[[1]]*j, w[[2]]}][b[n - i*j, i - 1]]; r = If[l[[1]] > r[[1]], l, If[l[[1]] == r[[1]], {0, l[[2]]}, 0] + r]]; r]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 0, 120}] (* Jean-François Alcover, Dec 21 2016, translated from Maple *)

#14 by Jean-François Alcover at Wed Dec 21 03:04:53 EST 2016

MATHEMATICA

STATUS

approved

editing

#13 by Alois P. Heinz at Mon Jan 04 22:34:33 EST 2016

STATUS

editing

approved

#12 by Alois P. Heinz at Mon Jan 04 22:34:08 EST 2016

EXAMPLE

a(11) = 1: [1,1,1,1,1,2,2,2] (product = 15).

#11 by Alois P. Heinz at Mon Jan 04 22:30:06 EST 2016

EXAMPLE

a(8) = 2: [1,1,1,1,1,1,1,1], [1,1,1,1,2,2] (product of multiplicities = 8).

#10 by Alois P. Heinz at Mon Jan 04 22:29:01 EST 2016

EXAMPLE

a(8) = 2: [1,1,1,1,1,1,1,1], [1,1,1,1,2,2] (product = 8).

a(9) = 1: [1,1,1,1,1,2,2] (product = 10).

a(10) = 2: [1,1,1,1,1,1,2,2], [1,1,1,1,2,2,2] (product = 12).

a(23) = 3: [1,1,1,1,1,1,1,1,1,2,2,2,2,3,3], [1,1,1,1,1,1,1,1,2,2,2,3,3,3], [1,1,1,1,1,1,2,2,2,2,3,3,3] (product = 72).

#9 by Alois P. Heinz at Mon Jan 04 22:24:22 EST 2016

EXAMPLE

a(10) = 2: [1,1,1,1,1,1,2,2], [1,1,1,1,2,2,2].