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

0,2

Comments

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

Links

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

Example

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}.

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 *)

Crossrefs

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

Sequence in context: A365698 A133523 A114805 * A181120 A000601 A062433

Adjacent sequences: A196719 A196720 A196721 * A196723 A196724 A196725

Keyword

nonn

Author

Alois P. Heinz, Oct 05 2011

Status

approved