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.

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, 360, 24, 8, 720, 30, 840, 32, 1260, 36, 9, 1680, 40, 2520, 48, 10, 5040, 60, 12, 6, 4, 3, 7560, 64, 10080, 72, 15120, 80, 20160, 84, 25200, 90, 27720, 96, 45360, 100

Offset: 3

Author

Davis Smith, Mar 15 2020

Keywords

• nonn
• tabf

Comments

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?

Examples

			The irregular triangle T(n,k) starts:
  n\k   0   1   2   3   4   ...
   3:   4   3
   4:   6   4   3
   5:  12   6   4   3
   6:  24   8
   7:  36   9
   8:  48  10
   9:  60  12   6   4   3
  10: 120  16
  11: 180  18
  12: 240  20
  13: 360  24   8
  ...
		

Links

• James Grime and Brady Haran, 5040 and other Anti-Prime Numbers, Numberphile video (2016).

Crossrefs

Cf. A000005, A002182, A002183, A189394.

Programs

PARI

A333328_rows(n)={my(N=Map(Mat([1,1;2,2;m=4,3])),p=2,F=[]); while(#Np,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}

Formula

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