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

1,2

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)

Links

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

Formula

a(p) = p for p = prime.

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

Example

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

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 *)

Prog

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

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).

Sequence in context: A369893 A345136 A128537 * A259209 A220849 A066841

Adjacent sequences: A266262 A266263 A266264 * A266266 A266267 A266268

Keyword

nonn

Author

Jaroslav Krizek, Dec 25 2015

Status

approved