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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
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.
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
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