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 A196720 Number of subsets of {1..n} (including empty set) such that the pairwise GCDs of elements are not distinct. 6
 1, 2, 4, 8, 13, 25, 33, 61, 81, 116, 140, 256, 282, 530, 606, 692, 823, 1551, 1653, 3173, 3391, 3805, 4177, 8049, 8345, 11524, 12508, 15294, 16204, 31692, 32048, 63280, 70834, 77224, 82048, 91686, 93597, 185245, 196109, 212359, 218223, 432495, 436031, 867647 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS All pairwise GCDs of each subset are equal if there are any. a(n) >= A084422(n). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..60 EXAMPLE a(5) = 25: {}, {1}, {2}, {3}, {4}, {5}, {1,2}, {1,3}, {1,4}, {1,5}, {2,3}, {2,4}, {2,5}, {3,4}, {3,5}, {4,5}, {1,2,3}, {1,2,5}, {1,3,4}, {1,3,5}, {1,4,5}, {2,3,5}, {3,4,5}, {1,2,3,5}, {1,3,4,5}. 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( 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..20); MATHEMATICA b[n_, s_] := b[n, s] = With[{m = Length[s], sn = Append[s, n]}, If[n<1, 1, b[n-1, s] + If[1 >= 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, 20}] (* Jean-François Alcover, Apr 06 2017, translated from Maple *) CROSSREFS Cf. A143823, A196719, A196721, A196722, A196723, A196724. Sequence in context: A262569 A248876 A102704 * A212906 A043774 A361818 Adjacent sequences: A196717 A196718 A196719 * A196721 A196722 A196723 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 05 2011 STATUS approved

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Last modified August 13 05:48 EDT 2024. Contains 375113 sequences. (Running on oeis4.)