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

1,1

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A360246 A242416 A360248 * A375934 A332785 A367589

Adjacent sequences: A317613 A317614 A317615 * A317617 A317618 A317619

Keyword

nonn

Author

Gus Wiseman, Aug 01 2018

Status

approved