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

1,2

Comments

A subsequence of A007916.

Links

Table of n, a(n) for n=1..63.

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A369254 A073085 A340657 * A119251 A182358 A336418

Adjacent sequences: A316790 A316791 A316792 * A316794 A316795 A316796

Keyword

nonn

Author

Gus Wiseman, Jul 14 2018

Status

approved