A136193 Irregular array read by rows: row n contains the products of each pair of consecutive positive divisors of n.

2, 3, 2, 8, 5, 2, 6, 18, 7, 2, 8, 32, 3, 27, 2, 10, 50, 11, 2, 6, 12, 24, 72, 13, 2, 14, 98, 3, 15, 75, 2, 8, 32, 128, 17, 2, 6, 18, 54, 162, 19, 2, 8, 20, 50, 200, 3, 21, 147, 2, 22, 242, 23, 2, 6, 12, 24, 48, 96, 288, 5, 125, 2, 26, 338, 3, 27, 243

Offset: 2

Author

Leroy Quet, Dec 20 2007; corrected Jan 20 2008

Keywords

• nonn
• tabf

Comments

The first listed row is row 2. Row n contains d(n)-1 (= A032741(n)) terms, where d(n) is the number of positive divisors of n.

Examples

			The positive divisors of 20 are 1,2,4,5,10,20. 1*2=2. 2*4=8. 4*5=20. 5*10=50. 10*20=200. So row 20 is (2,8,20,50,200).
The first few rows of the triangle are:
2;
3;
2, 8;
5;
2, 6, 18;
7;
2, 8, 32;
...
		

Crossrefs

Cf. A032741, A078730, A136195, A136181.

Programs

Maple

with(numtheory): a:=proc(n) local div: div:=divisors(n): seq(div[j]*div[j+1], j=1..tau(n)-1) end proc: for n from 2 to 25 do a(n) end do; # yields sequence as a two-dimensional array - Emeric Deutsch, Jan 08 2008

Mathematica

Flatten[Table[Times@@@Partition[Divisors[n],2,1],{n,30}]]  (* Harvey P. Dale, Apr 23 2011 *)

PARI

tabf(nn) = {for (n = 2, nn, d = divisors(n); for (i = 1, #d - 1, print1(d[i]*d[i+1], ", ");););} \\ Michel Marcus, Feb 10 2014

Extensions

More terms from Emeric Deutsch, Jan 08 2008

More terms from Michel Marcus, Feb 10 2014