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Positive divisors of n!, listed in increasing order for each n, a new row for each n.
41

%I #23 Sep 08 2022 08:45:08

%S 1,1,1,2,1,2,3,6,1,2,3,4,6,8,12,24,1,2,3,4,5,6,8,10,12,15,20,24,30,40,

%T 60,120,1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,

%U 90,120,144,180,240,360,720

%N Positive divisors of n!, listed in increasing order for each n, a new row for each n.

%C Elements per row: 1,1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)

%C This sequence is the same as A070861 for the first 38 terms, but differs thereafter.

%H Andrew Howroyd, <a href="/A079210/b079210.txt">Table of n, a(n) for n = 0..1979</a> (rows 0..12)

%e First few rows are:

%e 1;

%e 1;

%e 1,2;

%e 1,2,3,6;

%e 1,2,3,4,6,8,12,24;

%e 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120;

%e ...

%t Flatten[Table[Divisors[n!],{n,6}]] (* _Harvey P. Dale_, Mar 13 2011 *)

%o (Magma) [Divisors(Factorial(n)): n in [0..10]]; // _Vincenzo Librandi_, Jun 19 2015

%o (PARI) tabf(nn) = for (n=0, nn, print(divisors(n!))); \\ _Michel Marcus_, Jun 19 2015

%Y Cf. A027423 (row lengths), A062569 (row sums), A070861.

%K nonn,tabf

%O 0,4

%A Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

%E a(0)=1 prepended by _Andrew Howroyd_, Jan 26 2022