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A196719 Number of subsets of {1..n} (including empty set) such that the pairwise GCDs of elements are all distinct. 6
1, 2, 4, 7, 11, 16, 24, 31, 40, 52, 68, 79, 102, 115, 140, 175, 201, 218, 265, 284, 336, 396, 446, 469, 547, 599, 662, 742, 837, 866, 1034, 1065, 1153, 1275, 1370, 1511, 1719, 1756, 1869, 2030, 2244, 2285, 2613, 2656, 2865, 3236, 3394, 3441, 3780, 3921, 4232 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

EXAMPLE

a(6) = 24: {}, {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}, {3,4,6}.

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(

       igcd(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] = With[{m = Length[s], sn = Append[s, n]}, If[n<1, 1, b[n-1, s] + If[m*(m+1)/2 == Length[ Union @ Flatten @ Table[ Table[ GCD[ sn[[i]], sn[[j]]], {j, i+1, m+1}], {i, 1, m}]], 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, 50}] (* Jean-Fran├žois Alcover, Apr 06 2017, translated from Maple *)

CROSSREFS

Cf. A143823, A196720, A196721, A196722, A196723, A196724.

Sequence in context: A212364 A320591 A129339 * A011912 A063676 A099385

Adjacent sequences:  A196716 A196717 A196718 * A196720 A196721 A196722

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 05 2011

STATUS

approved

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Last modified October 20 07:33 EDT 2019. Contains 328252 sequences. (Running on oeis4.)