

A136193


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


1



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
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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 twodimensional 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



