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A225656
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a(n) = (1/n) * lcm(p1,p2,...,pk) for such a partition of n that this formula produces an integer and maximizes this value among all such partitions [p1,p2,...,pk] of n.
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5
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1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 5, 1, 6, 7, 1, 1, 10, 1, 21, 20, 15, 1, 35, 1, 30, 1, 55, 1, 154, 1, 1, 140, 105, 264, 385, 1, 210, 420, 693, 1, 780, 1, 1365, 1001, 420, 1, 1155, 1, 462, 3080, 3465, 1, 770, 6552, 6435, 5460, 1260, 1, 17017, 1, 2310, 12155
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OFFSET
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1,10
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LINKS
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FORMULA
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MAPLE
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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))[])/n:
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MATHEMATICA
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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&]]/n; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Jul 29 2015, after Alois P. Heinz *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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