A305567 Irregular triangle where T(n,k) is the number of finite sets of positive integers with least common multiple n and greatest common divisor k, where k runs over all divisors of n.

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 1, 1, 1, 1, 1, 32, 7, 2, 1, 1, 1, 1, 1, 7, 1, 1, 1, 7, 1, 1, 1, 8, 4, 2, 1, 1, 1, 1, 32, 2, 7, 1, 1, 1, 1, 1, 32, 7, 1, 2, 1, 1, 7, 1, 1, 1, 7, 1, 1, 1, 1, 1, 136, 32, 4, 7, 2, 1, 1, 1, 2

Offset: 1

Author

Gus Wiseman, Jun 05 2018

Keywords

• nonn
• tabf

Examples

			Triangle begins:
   1
   1  1
   1  1
   2  1  1
   1  1
   7  1  1  1
   1  1
   4  2  1  1
   2  1  1
   7  1  1  1
   1  1
  32  7  2  1  1  1
   1  1
   7  1  1  1
   7  1  1  1
   8  4  2  1  1
   1  1
  32  2  7  1  1  1
   1  1
  32  7  1  2  1  1
		

Crossrefs

Row lengths are A000005.

Cf. A076078, A181819, A281116, A285572, A290103, A304818, A305563, A305564, A305565, A305566.

Programs

Mathematica

Table[Length[Select[Subsets[Divisors[n]],And[GCD@@#==k,LCM@@#==n]&]],{n,30},{k,Divisors[n]}]