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%I #24 Oct 11 2021 04:49:15
%S 1,2,3,8,5,1,7,1,27,1,11,48,13,1,1,16,17,162,19,80,1,1,23,16,125,1,1,
%T 112,29,25,31,512,1,1,1,1944,37,1,1,25,41,49,43,176,405,1,47,48,343,
%U 1250,1,208,53,324,1,49,1,1,59,9,61,1,567,8,1,121,67,272,1,49,71,9,73,1
%N Let L(n) = ordered list of divisors of n = {d_1=1, d_2, ..., d_k=n}; set e_1=1, e_i = e_{i-1}/d_i if that is an integer otherwise e_i = e_{i-1}*d_i; then a(n) = e_k.
%C a(n) = r(n,tau(n)), where r is defined as follows:
%C let d(n,j) = j-th divisor of n, 1 <= j <= tau(n) = A000005(n), r(n,1)=d(n,1), r(n,j) = if d(n,j) divides r(n,j-1) then r(n,j-1)/d(n,j) else r(n,j-1)*d(n,j), 1 < j <= tau(n);
%C p prime: a(p)=p, a(p^2)=p^3, a(p^3)=1, a(p^k)=p^A008344(k+1);
%C a(m)=1 iff m multiplicatively perfect: a(A007422(k))=1.
%C a(A084111(n)) = A084111(n). - _Reinhard Zumkeller_, Jul 31 2014
%H Reinhard Zumkeller, <a href="/A084110/b084110.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DivisorProduct.html">Divisor Product</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativePerfectNumber.html">Multiplicative Perfect Number</a>.
%e Divisors of 48 = {1,2,3,4,6,8,12,16,24,48}: 1*2*3 = 6 -> 6*4 = 24 -> 24/6 = 4 -> 4*8 = 32 -> 32*12 = 384 -> 384/16 = 24 -> 24/24 = 1 -> 1*48 = a(48);
%e divisors of 49 = {1,7,49}: 1*7 = 7 -> 7*49 = 343 = a(49);
%e divisors of 50 = {1,2,5,10,25,50}: 1*2*5 = 10 -> 10/10 = 1 -> 1*25 = 25 -> 25*50 = 1250 = a(50).
%t a[n_] := Module[{d = Divisors[n], e}, e[i_] := e[i] = If[i == 1, 1, If[Divisible[e[i-1], d[[i]]], e[i-1]/d[[i]], e[i-1] d[[i]]]]; e[Length[d]]];
%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Oct 10 2021 *)
%o (Haskell)
%o a084110 = foldl (/*) 1 . a027750_row where
%o x /* y = if m == 0 then x' else x*y where (x',m) = divMod x y
%o -- _Reinhard Zumkeller_, Feb 21 2012, Oct 25 2010
%Y Cf. A027750, A084111 (fixed points), A084113, A084114.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, May 12 2003
%E Corrected and extended by _David Wasserman_, Dec 14 2004
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