A136179 a(n) = Product_{k=1..d(n)-1} gcd(b(k), b(k+1)), where b(k) is the k-th positive divisor of n and d(n) is the number of positive divisors of n.

1, 1, 1, 2, 1, 3, 1, 8, 3, 5, 1, 12, 1, 7, 5, 64, 1, 81, 1, 100, 7, 11, 1, 192, 5, 13, 27, 196, 1, 150, 1, 1024, 11, 17, 7, 1944, 1, 19, 13, 800, 1, 3087, 1, 484, 45, 23, 1, 12288, 7, 625, 17, 676, 1, 19683, 11, 1568, 19, 29, 1, 18000, 1, 31, 63, 32768, 13, 11979, 1, 1156, 23

Offset

1,4

Comments

a(n) is the product of the terms in row n of A136178.

Links

Diana Mecum, Table of n, a(n) for n = 1..796

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 a(20) = 1*2*1*5*10 = 100.

Mathematica

Table[Times @@ Map[GCD @@ # &, Partition[Divisors@ n, 2, 1]], {n, 69}] (* Michael De Vlieger, Sep 21 2017 *)

Prog

(PARI) a(n) = my(vd = divisors(n)); prod(k=1, #vd-1, gcd(vd[k], vd[k+1])); \\ Michel Marcus, Sep 22 2017

Crossrefs

Cf. A136178, A136180, A136182.

Sequence in context: A213074 A140966 A058036 * A185176 A198315 A126761

Adjacent sequences: A136176 A136177 A136178 * A136180 A136181 A136182

Keyword

nonn

Author

Leroy Quet, Dec 19 2007

Extensions

a(26) and beyond from Diana L. Mecum, Dec 29 2008

Status

approved