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A088881
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If A056239(m) = n, then a(n) is the maximum value of A000005(m).
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9
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1, 2, 3, 4, 6, 8, 10, 12, 16, 20, 24, 30, 36, 42, 48, 60, 72, 84, 96, 112, 128, 144, 168, 192, 224, 256, 288, 336, 384, 432, 480, 540, 600, 672, 768, 864, 960, 1080, 1200, 1320, 1440, 1620, 1800, 1980, 2160, 2400, 2640, 2880, 3240, 3600, 3960, 4320, 4800, 5280
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OFFSET
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0,2
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COMMENTS
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Maximum number of submultisets among all integer partitions of n. - Gus Wiseman, Jun 30 2019
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LINKS
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EXAMPLE
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The partition (3,2,1,1,1) has 16 submultisets, which is more than for any other partition of 8, so a(8) = 16. - Gus Wiseman, Jun 30 2019
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0 or i<2, n+1,
max(seq((j+1)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> b(n, n):
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MATHEMATICA
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$RecursionLimit = 1000; b[n_, i_] := b[n, i] = If[n == 0 || i<2, n+1, Max[Table[ (j+1)*b[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table [a[n], {n, 0, 100}] (* Jean-François Alcover, Apr 15 2015, after Alois P. Heinz *)
Table[Max@@(Times@@(1+Length/@Split[#])&)/@IntegerPartitions[n], {n, 0, 30}] (* Gus Wiseman, Jun 30 2019 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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