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A225655
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a(n) = largest LCM of partitions of n divisible by n.
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6
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1, 2, 3, 4, 5, 6, 7, 8, 9, 30, 11, 60, 13, 84, 105, 16, 17, 180, 19, 420, 420, 330, 23, 840, 25, 780, 27, 1540, 29, 4620, 31, 32, 4620, 3570, 9240, 13860, 37, 7980, 16380, 27720, 41, 32760, 43, 60060, 45045, 19320, 47, 55440, 49, 23100, 157080, 180180, 53
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OFFSET
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1,2
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COMMENTS
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a(n) = lcm(p1,p2,...,pk) for that partition of n for which the LCM is a multiple of n, and which maximizes this value among all such partitions [p1,p2,...,pk] of n.
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LINKS
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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))[]):
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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&]]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Jul 29 2015, after Alois P. Heinz *)
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CROSSREFS
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A225657 lists the values of n for which a(n) = n.
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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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