

A136179


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


4



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
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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, #vd1, 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



