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A181844
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Sum over all partitions of n of the LCM of the parts.
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9
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1, 1, 3, 6, 12, 23, 38, 73, 118, 198, 318, 530, 819, 1298, 1974, 2975, 4516, 6698, 9980, 14550, 21186, 30304, 43503, 62030, 87908, 123292, 172543, 239720, 331688, 458198, 629376, 860332, 1168172, 1583176, 2138438, 2876283, 3859770, 5159886, 6863702, 9112356
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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MAPLE
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with(combstruct):
a181844 := proc(n) local k, L, l, R, part;
R := NULL; L := 0;
for k from 1 to n do
part := iterstructs(Partition(n), size=k):
while not finished(part) do
l := nextstruct(part);
L := L + ilcm(op(l));
od;
od;
L end:
# second Maple program:
b:= proc(n, i, r) option remember; `if`(n=0, r, `if`(i<1, 0,
b(n, i-1, r)+b(n-i, min(i, n-i), ilcm(i, r))))
end:
a:= n-> b(n$2, 1):
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MATHEMATICA
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t[n_, k_] := LCM @@@ IntegerPartitions[n, {n - k + 1}] // Total; a[n_] := Sum[t[n, k], {k, 1, n}]; Table[a[n], {n, 1, 32}] (* Jean-François Alcover, Jul 26 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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