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%I #13 Jan 19 2023 14:25:47
%S 1,1,1,1,3,1,1,5,4,1,1,9,10,5,1,1,11,19,15,6,1,1,17,34,35,21,7,1,1,21,
%T 52,69,56,28,8,1,1,27,79,125,126,84,36,9,1,1,31,109,205,251,210,120,
%U 45,10,1,1,41,154,325,461,462,330,165,55,11,1,1,45,196
%N Regular triangle read by rows where T(n,k) is the number of relatively prime k-subsets of {1,...,n}, 1 <= k <= n.
%C Two or more numbers are relatively prime if they have no common divisor > 1. A single number is not considered to be relatively prime unless it is equal to 1.
%H Andrew Howroyd, <a href="/A320435/b320435.txt">Table of n, a(n) for n = 1..1275</a> (rows 1..50)
%F T(n,k) = Sum_{d=1..floor(n/k)} mu(d)*binomial(floor(n/d), k). - _Andrew Howroyd_, Jan 19 2023
%e Triangle begins:
%e 1
%e 1 1
%e 1 3 1
%e 1 5 4 1
%e 1 9 10 5 1
%e 1 11 19 15 6 1
%e 1 17 34 35 21 7 1
%e 1 21 52 69 56 28 8 1
%e 1 27 79 125 126 84 36 9 1
%e 1 31 109 205 251 210 120 45 10 1
%e 1 41 154 325 461 462 330 165 55 11 1
%e 1 45 196 479 786 923 792 495 220 66 12 1
%e 1 57 262 699 1281 1715 1716 1287 715 286 78 13 1
%e The T(6,2) = 11 sets are: {1,2}, {1,3}, {1,4}, {1,5}, {1,6}, {2,3}, {2,5}, {3,4}, {3,5}, {4,5}, {5,6}. Missing from this list are: {2,4}, {2,6}, {3,6}, {4,6}.
%t Table[Length[Select[Subsets[Range[n],{k}],GCD@@#==1&]],{n,10},{k,n}]
%o (PARI) T(n,k) = sum(d=1, n\k, moebius(d)*binomial(n\d, k)) \\ _Andrew Howroyd_, Jan 19 2023
%Y Row sums are A085945.
%Y Second column is A015614.
%Y Cf. A000837, A186974, A187106, A289508, A289509, A300486, A303139, A320424, A320436.
%K nonn,tabl
%O 1,5
%A _Gus Wiseman_, Jan 08 2019
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