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

2,1

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.

Links

Table of n, a(n) for n=2..69.

Example

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;
...

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 *)

Prog

(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

Crossrefs

Cf. A032741, A078730, A136195, A136181.

Sequence in context: A063708 A096488 A011280 * A187789 A245922 A098513

Adjacent sequences: A136190 A136191 A136192 * A136194 A136195 A136196

Keyword

nonn,tabf

Author

Leroy Quet, Dec 20 2007; corrected Jan 20 2008

Extensions

More terms from Emeric Deutsch, Jan 08 2008

More terms from Michel Marcus, Feb 10 2014

Status

approved