A083872 - OEIS

%I #11 Sep 18 2017 09:27:52

%S 1,2,3,6,4,8,12,24,5,10,15,20,30,40,60,120,9,16,18,36,45,48,72,80,90,

%T 144,180,240,360,720,7,14,21,28,35,42,56,63,70,84,105,112,126,140,168,

%U 210,252,280,315,336,420,504,560,630,840,1008,1260,1680,2520,5040,32,64

%N Triangle read by rows in which row n lists first appearance of m such that m divides n!.

%C Differs from A110797 starting at a(17)=9.

%C From _Rémy Sigrist_, Sep 17 2017: (Start)

%C Each number k > 0 appears exactly once in the triangle, on row A002034(k).

%C The n-th row of the triangle:

%C - contains A038024(n) terms,

%C - starts with A046021(n),

%C - ends with n! = A000142(n).

%C (End)

%H Rémy Sigrist, <a href="/A083872/b083872.txt">Rows n = 1..17, flattened</a>

%e 1!:1

%e 2!:1,2 -> 2 as 1 has already appeared

%e 3!:1,2,3,6 -> 3,6

%e 4!:1,2,3,4,6,8,12,24 -> 4,8,12,24

%t lst = {1}; Do[lst = Join[lst, Complement[Divisors[n!], Divisors[(n - 1)!]]], {n, 2, 9}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 07 2011 *)

%Y Cf. A000142, A002034, A038024, A046021.

%K nonn,tabf,look

%O 1,2

%A _Jon Perry_, Jun 18 2003

%E Extended by _Ray Chandler_, Aug 23 2005