A266265 Product of products of divisors of divisors of n.

1, 2, 3, 16, 5, 216, 7, 1024, 81, 1000, 11, 2985984, 13, 2744, 3375, 1048576, 17, 34012224, 19, 64000000, 9261, 10648, 23, 63403380965376, 625, 17576, 59049, 481890304, 29, 19683000000000, 31, 34359738368, 35937, 39304, 42875, 4738381338321616896, 37, 54872

Offset: 1

Author

Jaroslav Krizek, Dec 25 2015

Keywords

• nonn

Comments

a(n) = Product_{d|n} A007955(d) where A007955(m) = product of divisors of m.

From G. C. Greubel, Dec 31 2015: (Start)

for n>=1: 10^3|a(10*n), 10^6|a(20*n), 10^9|a(30*n).

for n>=0: 10^6|a(60*n+50), 10^9|a(60*n+70). (End)

Examples

			For n = 6; with b(n) = A007955(n); a(6) = b(1)*b(2)*b(3)*b(6) = 1*2*3*36 = 216.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1200

Crossrefs

Cf. A007955 (product of divisors of n), A175317 (sum of products of divisors of divisors of n), A206032 (product of sums of divisors of divisors of n).

Programs

Magma

[&*[&*[b: b in Divisors(d)]: d in Divisors(n)]: n in [1..100]]

Maple

A266265 := proc(n)
    mul( A007955(d),d=numtheory[divisors](n)) ;
end proc:
seq(A266265(n),n=1..10) ; # R. J. Mathar, Feb 13 2019

Mathematica

Table[Product[Times @@ Divisors@ d, {d, Divisors@ n}], {n, 38}] (* Michael De Vlieger, Dec 31 2015 *)

PARI

a(n) = {my(d = divisors(n)); prod(k=1, #d, dd = divisors(d[k]); prod(kk=1,#dd, dd[kk]));} \\ Michel Marcus, Dec 27 2015

Formula

a(p) = p for p = prime.

a(n) = Product_{d|n} d^tau(n/d). - Ridouane Oudra, Apr 09 2023