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A333328 Irregular triangle read by rows: T(n,0) = A002182(n) and T(n,k + 1) = A000005(T(n,k)), terminating at the first number which is not highly composite, n > 2. 0

%I

%S 4,3,6,4,3,12,6,4,3,24,8,36,9,48,10,60,12,6,4,3,120,16,180,18,240,20,

%T 360,24,8,720,30,840,32,1260,36,9,1680,40,2520,48,10,5040,60,12,6,4,3,

%U 7560,64,10080,72,15120,80,20160,84,25200,90,27720,96,45360,100

%N Irregular triangle read by rows: T(n,0) = A002182(n) and T(n,k + 1) = A000005(T(n,k)), terminating at the first number which is not highly composite, n > 2.

%C There are two questions related to this array: First, which rows have length greater than any previous row? Second, are there any rows which terminate at a k greater than 6?

%H James Grime and Brady Haran, <a href="https://www.youtube.com/watch?v=2JM2oImb9Qg">5040 and other Anti-Prime Numbers</a>, Numberphile video (2016).

%F T(n,0) = A002182(n), T(n,k) = A000005(T(n,k - 1)).

%e The irregular triangle T(n,k) starts:

%e n\k 0 1 2 3 4 ...

%e 3: 4 3

%e 4: 6 4 3

%e 5: 12 6 4 3

%e 6: 24 8

%e 7: 36 9

%e 8: 48 10

%e 9: 60 12 6 4 3

%e 10: 120 16

%e 11: 180 18

%e 12: 240 20

%e 13: 360 24 8

%e ...

%o (PARI) A333328_rows(n)={my(N=Map(Mat([1,1;2,2;m=4,3])),p=2,F=[]); while(#N<n,if(numdiv(m)>p,mapput(N,m,p=numdiv(m)); my(M=List([m,q=p])); while(mapisdefined(N,q,&q),listput(M,q));print(#N", "Vec(M)); F=concat(F,Vec(M))); my(s=if(m>=720720,360360,m>=5040,2520,m>=840,420,m>=60,60,2)); until(numdiv(m+=s)>p,));F}

%Y Cf. A000005, A002182, A002183, A189394.

%K nonn,tabf

%O 3,1

%A _Davis Smith_, Mar 15 2020

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Last modified June 21 16:20 EDT 2021. Contains 345364 sequences. (Running on oeis4.)