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A236309 Total number of distinct least common multiples of (i,j) with 1<=i

%I A236309 #21 Nov 07 2020 09:42:48
%S A236309 0,1,3,5,9,10,16,20,26,28,38,41,53,56,61,69,85,88,106,112,119,124,146,
%T A236309 151,171,177,195,203,231,235,265,281,293,301,319,328,364,373,387,399,
%U A236309 439,445,487,500,517,528,574,585,627,637,656,671,723,732,757,777,798
%N A236309 Total number of distinct least common multiples of (i,j) with 1<=i<j<=n.
%H A236309 Alois P. Heinz, <a href="/A236309/b236309.txt">Table of n, a(n) for n = 1..1000</a>
%e A236309 For n=10, 1<=i<j<=10, there are 28 distinct [i,j], i.e. 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 63, 70, 72, 90.
%e A236309 Hence a(10) = 28.
%p A236309 b:= proc(n) b(n):= {seq(ilcm(i, n), i=1..n-1)} end:
%p A236309 s:= proc(n) s(n):= `if`(n=0, {}, b(n) union s(n-1)) end:
%p A236309 a:= n-> nops(s(n)):
%p A236309 seq(a(n), n=1..80);  # _Alois P. Heinz_, Apr 29 2014
%t A236309 a[n_] := Table[LCM[i, j], {i, 1, n-1}, {j, i+1, n}] // Flatten // Union // Length;
%t A236309 Array[a, 100] (* _Jean-François Alcover_, Nov 07 2020 *)
%Y A236309 Cf. A202479.
%K A236309 nonn
%O A236309 1,3
%A A236309 _Han Hu_, Apr 22 2014
%E A236309 More terms from _Alois P. Heinz_, Apr 29 2014