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

1,6

Links

Table of n, a(n) for n=1..85.

Example

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

Mathematica

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

Crossrefs

Row lengths are A000005.

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

Sequence in context: A380164 A174215 A364457 * A134744 A260875 A351350

Adjacent sequences: A305564 A305565 A305566 * A305568 A305569 A305570

Keyword

nonn,tabf

Author

Gus Wiseman, Jun 05 2018

Status

approved