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A196722 Number of subsets of {1..n} (including empty set) such that the pairwise LCMs of elements are not distinct. 6
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Apr 12 2017, translated from Maple *)

CROSSREFS

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

Sequence in context: A131075 A133523 A114805 * A181120 A000601 A062433

Adjacent sequences:  A196719 A196720 A196721 * A196723 A196724 A196725

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 05 2011

STATUS

approved

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Last modified April 17 11:50 EDT 2021. Contains 343064 sequences. (Running on oeis4.)