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A225652
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a(n) = (1/n) * lcm(n,p1,p2,...,pk) for that partition of n which maximizes this value among all partitions [p1,p2,...,pk] of n.
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6
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1, 1, 2, 3, 6, 5, 12, 15, 20, 21, 30, 35, 60, 45, 56, 105, 210, 77, 420, 99, 220, 315, 840, 385, 924, 1155, 1540, 585, 2520, 364, 4620, 3465, 3640, 4620, 3432, 5005, 13860, 8190, 6160, 9009, 30030, 4290, 60060, 9945, 12376, 45045, 120120, 17017, 51480, 36036
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OFFSET
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1,3
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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(seq(ilcm(n, i), i=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, {}, Table[Map[Function[{x}, LCM[x, If[j==0, 1, i]]], b[n-i*j, i-1]], {j, 0, n/i}]]]; a[n_] := Max[Table[LCM[n, i], {i, b[n, n]}]]/n; Table[Print["a(", n, ") = ", an = a[n]]; an, {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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