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Search: id:A007955
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| A007955 |
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Product of divisors of n. |
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+0
39
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| 1, 2, 3, 8, 5, 36, 7, 64, 27, 100, 11, 1728, 13, 196, 225, 1024, 17, 5832, 19, 8000, 441, 484, 23, 331776, 125, 676, 729, 21952, 29, 810000, 31, 32768, 1089, 1156, 1225, 10077696, 37, 1444, 1521, 2560000, 41, 3111696, 43, 85184, 91125, 2116, 47
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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All terms of this sequence occur only once. See the link for a proof. - T. D. Noe (noe(AT)sspectra.com), Jul 07 2008
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REFERENCES
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M. Le, On Smarandache Divisor Products, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, 144-145.
F. Smarandache, "Only Problems, not Solutions!", Xiquan Publ., Phoenix-Chicago, 1993.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
F. Smarandache, Only Problems, Not Solutions!.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
T. D. Noe, The Divisor Product is Unique
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FORMULA
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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).
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MAPLE
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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;
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MATHEMATICA
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Array [ Times @@ Divisors[ # ]&, 100 ]
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PROGRAM
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(MAGMA) f := function(n); t1 := &*[d : d in Divisors(n) ]; return t1; end function;
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CROSSREFS
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Cf. A000005, A007956.
Sequence in context: A117987 A091136 A140651 this_sequence A162537 A109844 A128779
Adjacent sequences: A007952 A007953 A007954 this_sequence A007956 A007957 A007958
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KEYWORD
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nonn,nice
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AUTHOR
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R. Muller
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