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

0, 1, 3, 5, 9, 10, 16, 20, 26, 28, 38, 41, 53, 56, 61, 69, 85, 88, 106, 112, 119, 124, 146, 151, 171, 177, 195, 203, 231, 235, 265, 281, 293, 301, 319, 328, 364, 373, 387, 399, 439, 445, 487, 500, 517, 528, 574, 585, 627, 637, 656, 671, 723, 732, 757, 777, 798

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Example

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.
Hence a(10) = 28.

Maple

b:= proc(n) b(n):= {seq(ilcm(i, n), i=1..n-1)} end:
s:= proc(n) s(n):= `if`(n=0, {}, b(n) union s(n-1)) end:
a:= n-> nops(s(n)):
seq(a(n), n=1..80);  # Alois P. Heinz, Apr 29 2014

Mathematica

a[n_] := Table[LCM[i, j], {i, 1, n-1}, {j, i+1, n}] // Flatten // Union // Length;
Array[a, 100] (* Jean-François Alcover, Nov 07 2020 *)

Crossrefs

Cf. A202479.

Sequence in context: A316296 A344293 A063038 * A304588 A335058 A066769

Adjacent sequences: A236306 A236307 A236308 * A236310 A236311 A236312

Keyword

nonn

Author

Han Hu, Apr 22 2014

Extensions

More terms from Alois P. Heinz, Apr 29 2014

Status

approved