A293511 Numbers that can be written as a product of distinct squarefree numbers in exactly one way.

1, 2, 3, 5, 7, 11, 12, 13, 17, 18, 19, 20, 23, 28, 29, 31, 36, 37, 41, 43, 44, 45, 47, 50, 52, 53, 59, 61, 63, 67, 68, 71, 73, 75, 76, 79, 83, 89, 92, 97, 98, 99, 100, 101, 103, 107, 109, 113, 116, 117, 120, 124, 127, 131, 137, 139, 147, 148, 149, 151, 153

Offset: 1

Author

Gus Wiseman, Oct 11 2017

Keywords

• nonn

Comments

First differs from A212166 at a(128) = 363, A212166(128) = 360.

Examples

			360 is not in the sequence because it has two possible expressions: 2*3*6*10 or 2*6*30.
		

Crossrefs

Cf. A001055, A005117, A045778, A050320, A050326, A292432, A292444, A293243.

Programs

Mathematica

nn=300;
sqfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[sqfacs[n/d],Min@@#>d&]],{d,Select[Rest[Divisors[n]],SquareFreeQ]}]];
Select[Range[nn],Length[sqfacs[#]]===1&]