A305567 - OEIS

%I #4 Jun 05 2018 22:36:19

%S 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,

%T 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,

%U 1,1,1,7,1,1,1,1,1,136,32,4,7,2,1,1,1,2

%N 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.

%e Triangle begins:

%e    1

%e    1  1

%e    1  1

%e    2  1  1

%e    1  1

%e    7  1  1  1

%e    1  1

%e    4  2  1  1

%e    2  1  1

%e    7  1  1  1

%e    1  1

%e   32  7  2  1  1  1

%e    1  1

%e    7  1  1  1

%e    7  1  1  1

%e    8  4  2  1  1

%e    1  1

%e   32  2  7  1  1  1

%e    1  1

%e   32  7  1  2  1  1

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

%Y Row lengths are A000005.

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

%K nonn,tabf

%O 1,6

%A _Gus Wiseman_, Jun 05 2018