A136178 - OEIS

%I #16 Sep 22 2017 03:50:47

%S 1,1,1,2,1,1,1,3,1,1,2,4,1,3,1,1,5,1,1,1,1,2,6,1,1,1,7,1,1,5,1,2,4,8,

%T 1,1,1,3,3,9,1,1,2,1,5,10,1,1,7,1,1,11,1,1,1,1,2,2,4,12,1,5,1,1,13,1,

%U 3,9,1,2,1,7,14,1,1,1,1,1,2,5,15,1,1,2,4,8,16,1,1,11,1,1,17,1,1,7,1,1,1,2,3

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

%C Each row has d(n)-1 terms, where d(n) is the number of positive divisors of n. The first row listed is row 2.

%H Michael De Vlieger, <a href="/A136178/b136178.txt">Table of n, a(n) for n = 2..15955</a> (rows 2 <= n <= 2310)

%e The positive divisors of 20 are 1,2,4,5,10,20. GCD(1,2)=1. GCD(2,4)=2. GCD(4,5)=1. GCD(5,10)=5. And GCD(10,20)=10. So row 20 is (1,2,1,5,10).

%e From _R. J. Mathar_, Jul 20 2009: (Start)

%e The table starts

%e 1

%e 1

%e 1,2

%e 1

%e 1,1,3

%e 1

%e 1,2,4

%e 1,3

%e 1,1,5

%e 1

%e 1,1,1,2,6

%e (End)

%p A136178row := proc(n) local dvs; dvs := sort(convert(numtheory[divisors](n),list)) ; seq(gcd(op(d-1,dvs),op(d,dvs)),d=2..nops(dvs)) ; end: seq(A136178row (n),n=1..70) ; # _R. J. Mathar_, Jul 20 2009

%t Table[Map[GCD @@ # &, Partition[Divisors@ n, 2, 1]], {n, 2, 36}] // Flatten (* _Michael De Vlieger_, Sep 21 2017 *)

%o (PARI) row(n) = my(d=divisors(n)); vector(#d-1, k, gcd(d[k], d[k+1]));

%o tabf(nn) = for(n=2, nn, print(row(n))); \\ _Michel Marcus_, Sep 22 2017

%Y Cf. A136179, A136180, A136181.

%K nonn,tabf

%O 2,4

%A _Leroy Quet_, Dec 19 2007

%E Keyword:tabl replaced with keyword:tabf by _R. J. Mathar_, Jul 22 2009

%E Extended beyond row 10 by _R. J. Mathar_, Jul 20 2009