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A317616
Numbers whose prime multiplicities are not pairwise indivisible.
5
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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 01 2018
STATUS
approved