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URL: https://oeis.org/A266265

⇱ A266265 - OEIS

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A266265
Product of products of divisors of divisors of n.
11
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
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Dec 25 2015
STATUS
approved