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Search: id:A061538
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| A061538 |
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Product of all divisors of n, divided by product of unitary divisors; or equivalently product of non-unitary divisors of n. |
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+0
5
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| 1, 1, 1, 2, 1, 1, 1, 8, 3, 1, 1, 12, 1, 1, 1, 64, 1, 18, 1, 20, 1, 1, 1, 576, 5, 1, 27, 28, 1, 1, 1, 1024, 1, 1, 1, 7776, 1, 1, 1, 1600, 1, 1, 1, 44, 45, 1, 1, 110592, 7, 50, 1, 52, 1, 2916, 1, 3136, 1, 1, 1, 3600, 1, 1, 63, 32768, 1, 1, 1, 68, 1, 1, 1, 26873856, 1, 1, 75, 76, 1, 1, 1
(list; graph; listen)
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OFFSET
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1,4
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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a(n)=n^(A048105(n)/2)=n^[(A000005(n)-A034444(n))/2]
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EXAMPLE
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n=16 and only {1,16} are unitary, while {2,4,8} are non-unitary divisors, so a(16)=64. When all divisors are unitary, then A048105 is 0 and corresponding terms here are equal to 1.
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PROGRAM
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(PARI) { for (n=1, 1000, s=divisors(n); a=1; for (i=2, length(s), d=s[i]; if (gcd(d, n/d)!=1, a*=d)); write("b061538.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 24 2009]
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CROSSREFS
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A000005, A034444, A007955, A048105, A007955, A007956.
Sequence in context: A011127 A171660 A157117 this_sequence A123602 A065521 A156188
Adjacent sequences: A061535 A061536 A061537 this_sequence A061539 A061540 A061541
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), May 15 2001
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EXTENSIONS
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Corrected and edited by Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 05 2009
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