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A354756
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a(n) is the number of permutations p of [n] such that lcm(i, p(i)) <= n for all i in [n].
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0
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1, 1, 2, 3, 8, 10, 56, 64, 192, 332, 1184, 1264, 12192, 12872, 37568, 100836, 311760, 322320, 2338368, 2408848, 14433408, 32058912, 76931008, 78528704, 919469408, 1158792224, 2689828672, 4675217824, 21679173184, 21984820864, 381078324992, 386159441600
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OFFSET
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0,3
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LINKS
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MAPLE
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b:= proc(s, m) option remember; `if`(s={}, 1, add(
`if`(ilcm(nops(s), i)>m, 0, b(s minus {i}, m)), i=s))
end:
a:= n-> b({$1..n}, n):
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MATHEMATICA
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b[s_, m_] := b[s, m] = If[s == {}, 1, Sum[
If[LCM[Length[s], i]>m, 0, b[s~Complement~{i}, m]], {i, s}]];
a[n_] := b[Range[n], n];
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PROG
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(PARI) a(n) = {my(nb=0); for (i=1, n!, my(p=numtoperm(n, i), ok=1); for (k=1, #p, if (lcm(k, p[k]) > n, ok = 0; break); ); if (ok, nb++); ); nb; }
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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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