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A084110
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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.
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11
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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, 112, 29, 25, 31, 512, 1, 1, 1, 1944, 37, 1, 1, 25, 41, 49, 43, 176, 405, 1, 47, 48, 343, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) = r(n,tau(n)), where r is defined as follows:
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);
p prime: a(p)=p, a(p^2)=p^3, a(p^3)=1, a(p^k)=p^A008344(k+1);
a(m)=1 iff m multiplicatively perfect: a(A007422(k))=1.
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..10000 [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 25 2010]
Eric Weisstein's World of Mathematics, Divisor Product.
Eric Weisstein's World of Mathematics, Multipl icative Perfect Number.
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EXAMPLE
| 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);
divisors of 49 = {1,7,49}: 1*7=7 -> 7*49=343=a(49);
divisors of 50 = {1,2,5,10,25,50}: 1*2*5=10 -> 10/10=1 -> 1*25=25 -> 25*50=1250=a(50).
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PROG
| Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 25 2010: (Start)
(Other) Haskell:
(/*) x y = if x `mod` y == 0 then x `div` y else x*y
a084110 n = foldl (/*) 1 $ filter ((== 0) . mod n) [1..n]
-- eop. (End)
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CROSSREFS
| Cf. A027750, A084111, A084113, A084114, X000D-M.
Sequence in context: A194931 A195248 A202651 * A192646 A100208 A093928
Adjacent sequences: A084107 A084108 A084109 * A084111 A084112 A084113
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 12 2003
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EXTENSIONS
| Corrected and extended by David Wasserman (wasserma(AT)spawar.navy.mil), Dec 14 2004
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