A136193 - OEIS

%I #13 Apr 09 2014 10:17:01

%S 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,

%T 15,75,2,8,32,128,17,2,6,18,54,162,19,2,8,20,50,200,3,21,147,2,22,242,

%U 23,2,6,12,24,48,96,288,5,125,2,26,338,3,27,243

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

%C 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.

%e 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).

%e The first few rows of the triangle are:

%e 2;

%e 3;

%e 2, 8;

%e 5;

%e 2, 6, 18;

%e 7;

%e 2, 8, 32;

%e ...

%p 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

%t Flatten[Table[Times@@@Partition[Divisors[n],2,1],{n,30}]]  (* _Harvey P. Dale_, Apr 23 2011 *)

%o (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

%Y Cf. A032741, A078730, A136195, A136181.

%K nonn,tabf

%O 2,1

%A _Leroy Quet_, Dec 20 2007; corrected Jan 20 2008

%E More terms from _Emeric Deutsch_, Jan 08 2008

%E More terms from _Michel Marcus_, Feb 10 2014