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A196721 Number of subsets of {1..n} (including empty set) such that the pairwise LCMs of elements are all distinct. 6
1, 2, 4, 8, 14, 28, 42, 84, 132, 236, 352, 704, 920, 1840, 2736, 3816, 5700, 11400, 15384, 30768, 39552, 54656, 81672, 163344, 196176, 362656, 542304, 930352, 1195168, 2390336, 2914304, 5828608, 8513920, 11674848, 17490432, 23484224, 28058816, 56117632, 84100800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..50

EXAMPLE

a(4) = 14: {}, {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,2,3}, {1,3,4}, {2,3,4}.

MAPLE

b:= proc(n, s) local sn, m;

      m:= nops(s);

      sn:= [s[], n];

      `if`(n<1, 1, b(n-1, s) +`if`(m*(m+1)/2 = nops(({seq(seq(

       ilcm(sn[i], sn[j]), j=i+1..m+1), i=1..m)})), b(n-1, sn), 0))

    end:

a:= proc(n) option remember;

      b(n-1, [n]) +`if`(n=0, 0, a(n-1))

    end:

seq(a(n), n=0..10);

MATHEMATICA

b[n_, s_] := b[n, s] = Module[{sn, m}, m = Length[s]; sn = Append[s, n]; If[n < 1, 1, b[n - 1, s] + If[m*(m + 1)/2 == Length @ Union @ Flatten @ Table[LCM [sn[[i]], sn[[j]]], {i, 1, m}, {j, i+1, m+1}], b[n-1, sn], 0]]]; a[n_] := a[n] = b[n-1, {n}] + If[n == 0, 0, a[n-1]]; Table[ Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Feb 02 2017, translated from Maple *)

CROSSREFS

Cf. A143823, A196719, A196720, A196722, A196723, A196724.

Sequence in context: A321402 A210669 A122026 * A118034 A096590 A068912

Adjacent sequences:  A196718 A196719 A196720 * A196722 A196723 A196724

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 05 2011

EXTENSIONS

Terms a(31) and beyond from Fausto A. C. Cariboni, Oct 18 2020

STATUS

approved

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Last modified April 19 00:18 EDT 2021. Contains 343098 sequences. (Running on oeis4.)