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A316793 Numbers whose prime multiplicities are distinct and relatively prime. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A307714 A073085 A340657 * A119251 A182358 A336418

Adjacent sequences:  A316790 A316791 A316792 * A316794 A316795 A316796

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 14 2018

STATUS

approved

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Last modified April 23 12:15 EDT 2021. Contains 343204 sequences. (Running on oeis4.)