[seqfan] Re: Composites in the i*j multplication table A333996

Marc LeBrun mlb at well.com
Fri Oct 2 23:06:06 CEST 2020


Doh!  It's even more confused, since it says *composites* -- so presumably it'd need to *exclude* the non-composites 1, 2, 3, 5... which appear only in the 1Xn and nX1 cells...
So it would start 0,0,1,3,6,... (perhaps this is what you were saying, Richard?)

> On Oct 2, 2020, at 9:52 AM, Marc LeBrun <mlb at well.com> wrote:
> 
> I agree, seems confused: A333996 & A334454 currently have identical names,
> "Number of distinct composite numbers in the n X n multiplication table.",
> yet different values.  And shouldn't the offsets be 0 (not 1) in any case?
> 
> Moreover, shouldn't it start 0, 1, 3, 6, 9,...?  From the cardinalities of
> {}
> {1}
> {1,2,4}
> {1,2,4,3,6,9}
> {1,2,4,3,6,9,8,12,16}
> ...
> 
> 
>> On Oct 2, 2020, at 3:51 AM, Richard J. Mathar <mathar at mpia-hd.mpg.de> wrote:
>> 
>> Does someone understand the a(4)=7 in the A333996(4) count
>> for composites in the 4x4 multiplication table?
>> I get a(4)=6, that is the cardinality of {4,6,8,9,12,16},
>> and a sequence like 0, 1, 3, 6, 10, 14, 20, 25, 31, 37...
>> See also A027424 (cardinality of the set of all i*j) and A000720
>> (number of primes in the multiplication table).
>> 
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> 
> 
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