A136178 Irregular array read by rows: row n contains the GCDs of each pair of consecutive positive divisors of n.

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, 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, 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

Offset

2,4

Comments

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.

Links

Michael De Vlieger, Table of n, a(n) for n = 2..15955 (rows 2 <= n <= 2310)

Example

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).
From R. J. Mathar, Jul 20 2009: (Start)
The table starts
1
1
1,2
1
1,1,3
1
1,2,4
1,3
1,1,5
1
1,1,1,2,6
(End)

Maple

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

Mathematica

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

Prog

(PARI) row(n) = my(d=divisors(n)); vector(#d-1, k, gcd(d[k], d[k+1]));
tabf(nn) = for(n=2, nn, print(row(n))); \\ Michel Marcus, Sep 22 2017

Crossrefs

Cf. A136179, A136180, A136181.

Sequence in context: A309939 A111603 A180178 * A047140 A047150 A280489

Adjacent sequences: A136175 A136176 A136177 * A136179 A136180 A136181

Keyword

nonn,tabf

Author

Leroy Quet, Dec 19 2007

Extensions

Keyword:tabl replaced with keyword:tabf by R. J. Mathar, Jul 22 2009

Extended beyond row 10 by R. J. Mathar, Jul 20 2009

Status

approved