A196722 Number of subsets of {1..n} (including empty set) such that the pairwise LCMs of elements are not distinct.

1, 2, 4, 7, 11, 16, 23, 30, 38, 47, 58, 69, 83, 96, 111, 128, 144, 161, 181, 200, 223, 246, 269, 292, 319, 344, 371, 398, 429, 458, 496, 527, 559, 594, 629, 668, 708, 745, 784, 825, 870, 911, 962, 1005, 1052, 1102, 1149, 1196, 1248, 1297, 1349, 1402, 1457, 1510

Offset: 0

Author

Alois P. Heinz, Oct 05 2011

Keywords

• nonn

Comments

All pairwise LCMs of each subset are equal if there are any.

Examples

			A(6) = 23: {}, {1}, {2}, {3}, {4}, {5}, {6}, {1,2}, {1,3}, {1,4}, {1,5}, {1,6}, {2,3}, {2,4}, {2,5}, {2,6}, {3,4}, {3,5}, {3,6}, {4,5}, {4,6}, {5,6}, {2,3,6}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A143823, A196719, A196720, A196721, A196723, A196724.

Programs

Maple

b:= proc(n, s) local sn, m;
      m:= nops(s);
      sn:= [s[], n];
      `if`(n<1, 1, b(n-1, s) +`if`(1 >= 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..50);

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[1 >= 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[a[n], {n, 0, 60}] (* Jean-François Alcover, Apr 12 2017, translated from Maple *)