cp's OEIS Frontend

A266265 Product of products of divisors of divisors of n.

%I A266265 #27 Apr 09 2023 15:31:26
%S A266265 1,2,3,16,5,216,7,1024,81,1000,11,2985984,13,2744,3375,1048576,17,
%T A266265 34012224,19,64000000,9261,10648,23,63403380965376,625,17576,59049,
%U A266265 481890304,29,19683000000000,31,34359738368,35937,39304,42875,4738381338321616896,37,54872
%N A266265 Product of products of divisors of divisors of n.
%C A266265 a(n) = Product_{d|n} A007955(d) where A007955(m) = product of divisors of m.
%C A266265 From _G. C. Greubel_, Dec 31 2015: (Start)
%C A266265 for n>=1: 10^3|a(10*n), 10^6|a(20*n), 10^9|a(30*n).
%C A266265 for n>=0: 10^6|a(60*n+50), 10^9|a(60*n+70). (End)
%H A266265 G. C. Greubel, <a href="/A266265/b266265.txt">Table of n, a(n) for n = 1..1200</a>
%F A266265 a(p) = p for p = prime.
%F A266265 a(n) = Product_{d|n} d^tau(n/d). - _Ridouane Oudra_, Apr 09 2023
%e A266265 For n = 6; with b(n) = A007955(n); a(6) = b(1)*b(2)*b(3)*b(6) = 1*2*3*36 = 216.
%p A266265 A266265 := proc(n)
%p A266265     mul( A007955(d),d=numtheory[divisors](n)) ;
%p A266265 end proc:
%p A266265 seq(A266265(n),n=1..10) ; # _R. J. Mathar_, Feb 13 2019
%t A266265 Table[Product[Times @@ Divisors@ d, {d, Divisors@ n}], {n, 38}] (* _Michael De Vlieger_, Dec 31 2015 *)
%o A266265 (Magma) [&*[&*[b: b in Divisors(d)]: d in Divisors(n)]: n in [1..100]]
%o A266265 (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
%Y A266265 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).
%K A266265 nonn
%O A266265 1,2
%A A266265 _Jaroslav Krizek_, Dec 25 2015