A317616 Numbers whose prime multiplicities are not pairwise indivisible.

12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 68, 75, 76, 80, 84, 88, 90, 92, 96, 98, 99, 104, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 144, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189, 192

Offset: 1

Author

Gus Wiseman, Aug 01 2018

Keywords

• nonn

Comments

The numbers of terms that do not exceed 10^k, for k = 2, 3, ..., are 26, 344, 3762, 38711, 390527, 3915874, 39192197, 392025578, 3920580540, ... . Apparently, the asymptotic density of this sequence exists and equals 0.392... . - Amiram Eldar, Sep 25 2024

Examples

			72 = 2^3 * 3^2 is not in the sequence because 3 and 2 are pairwise indivisible.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A118914, A124010, A285572, A285573, A303362, A304713, A316475, A317101, A317102.

Programs

Mathematica

Select[Range[100],!Select[Tuples[Last/@FactorInteger[#],2],And[UnsameQ@@#,Divisible@@#]&]=={}&]

PARI

is(k) = if(k == 1, 0, my(e = Set(factor(k)[,2])); if(vecmax(e) == 1, 0, for(i = 1, #e, for(j = 1, i-1, if(!(e[i] % e[j]), return(1)))); 0)); \\ Amiram Eldar, Sep 25 2024