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Search: id:A056623
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| A056623 |
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Largest unitary square divisor of n: if n=LLgggf (see A056192) and a(n)=LL, then its complementary divisor n/LL =gggf and GCD[L^2,n/LL]=1. |
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1
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| 1, 1, 1, 4, 1, 1, 1, 1, 9, 1, 1, 4, 1, 1, 1, 16, 1, 9, 1, 4, 1, 1, 1, 1, 25, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 36, 1, 1, 1, 1, 1, 1, 1, 4, 9, 1, 1, 16, 49, 25, 1, 4, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 9, 64, 1, 1, 1, 4, 1, 1, 1, 9, 1, 1, 25, 4, 1, 1, 1, 16, 81, 1, 1, 4, 1, 1, 1, 1, 1, 9, 1, 4, 1, 1, 1, 4, 1, 49, 9
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OFFSET
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1,4
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FORMULA
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a(n)=A008833[n]/A055229[n]^2 =K^2/g^2, which coincides with the largest square divisor iff the g-factor is 1.
Multiplicative with a(p^e)=p^e for even e, a(p)=1, a(p^e)=p^(e-3) for odd e>1. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 30 2002
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EXAMPLE
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n=250: largest square divisor is 25, but is not unitary. GCD[25,10]=5=A055229(250)=g, so a(250)=25/g^2=1. The largest square and unitary divisor is here 1; n=200, A008833(200)=100, A055229(200)=g=GCD[100,2]=2 so a(200)=100/2^2=25 is already unitary because GCD[25,200/25]=1.
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CROSSREFS
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A008833, A055229, A000188, A046951, A034444, A056192.
Adjacent sequences: A056620 A056621 A056622 this_sequence A056624 A056625 A056626
Sequence in context: A046591 A119350 A016528 this_sequence A038025 A079982 A039927
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KEYWORD
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nonn,mult
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Aug 08 2000
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