Search: id:A007955
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%I A007955
%S A007955 1,2,3,8,5,36,7,64,27,100,11,1728,13,196,225,1024,17,5832,19,8000,441,
%T A007955 484,23,331776,125,676,729,21952,29,810000,31,32768,1089,1156,1225,
%U A007955 10077696,37,1444,1521,2560000,41,3111696,43,85184,91125,2116,47
%N A007955 Product of divisors of n.
%C A007955 All terms of this sequence occur only once. See the link for a proof. 
               - T. D. Noe (noe(AT)sspectra.com), Jul 07 2008
%D A007955 M. Le, On Smarandache Divisor Products, Smarandache Notions Journal, 
               Vol. 10, No. 1-2-3, 1999, 144-145.
%D A007955 F. Smarandache, "Only Problems, not Solutions!", Xiquan Publ., Phoenix-Chicago, 
               1993.
%H A007955 T. D. Noe, <a href="b007955.txt">Table of n, a(n) for n = 1..1000</a>
%H A007955 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">
               Only Problems, Not Solutions!</a>.
%H A007955 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DivisorProduct.html">Link to a section of The World of Mathematics.</
               a>
%H A007955 T. D. Noe, <a href="http://www.sspectra.com/math/DivisorProduct.pdf">
               The Divisor Product is Unique</a>
%F A007955 a(n)=n^(d(n)/2)=n^(A000005(n)/2). Since a(n) = product_(d|n); d = product_(d|n); 
               n/d, we have a(n)*a(n)= product_(d|n); d*(n/d) = product_(d|n); n 
               = n^(tau(n)), whence a(n)=n^(tau(n)/2).
%p A007955 with(numtheory): A007955 := proc(n) local i,t1,t2,t3; t3 := convert(divisors(n),
               list); t2 := nops(t3); t1 := mul(t3[i],i=1..t2); end;
%t A007955 Array [ Times @@ Divisors[ # ]&, 100 ]
%o A007955 (MAGMA) f := function(n); t1 := &*[d : d in Divisors(n) ]; return t1; 
               end function;
%Y A007955 Cf. A000005, A007956.
%Y A007955 Sequence in context: A117987 A091136 A140651 this_sequence A162537 A109844 
               A128779
%Y A007955 Adjacent sequences: A007952 A007953 A007954 this_sequence A007956 A007957 
               A007958
%K A007955 nonn,nice
%O A007955 1,2
%A A007955 R. Muller

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