A316793 Numbers whose prime multiplicities are distinct and relatively prime.

1, 2, 3, 5, 7, 11, 12, 13, 17, 18, 19, 20, 23, 24, 28, 29, 31, 37, 40, 41, 43, 44, 45, 47, 48, 50, 52, 53, 54, 56, 59, 61, 63, 67, 68, 71, 72, 73, 75, 76, 79, 80, 83, 88, 89, 92, 96, 97, 98, 99, 101, 103, 104, 107, 108, 109, 112, 113, 116, 117, 124, 127, 131

Offset: 1

Author

Gus Wiseman, Jul 14 2018

Keywords

• nonn

Comments

A subsequence of A007916.

Examples

			60 = 2^2 * 3^1 * 5^1 has prime multiplicities (2,1,1), which are relatively prime but not distinct, so 60 does not belong to the sequence.
72 = 2^3 * 3^2 has prime multiplicities (3,2), which are distinct and relatively prime, so 72 belongs to the sequence.
144 = 2^4 * 3^2 has prime multiplicities (4,2), which are distinct but not relatively prime, so 144 does not belong to the sequence.
		

Crossrefs

Cf. A000837, A005117, A007916, A130091, A301700, A303431, A316794, A316795, A316796.

Programs

Mathematica

Select[Range[100],And[UnsameQ@@Last/@FactorInteger[#],GCD@@Last/@FactorInteger[#]==1]&]