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Search: id:A056191
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| A056191 |
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Characteristic cube divisor of n: cube of g=GCD[K,F], where K is the largest square root divisor of n (A000188) and F=n/(K*K)=A007913(n) is its square-free part; g^2 divides K^2=A008833(n)=g^2*L^2 and g divides F=gf. |
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4
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| 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 27, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1
(list; graph; listen)
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OFFSET
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1,8
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COMMENT
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This is not the largest cube which divides n. It is canonical, since the decomposition n=KKgggf is unique (factors are defined above and dependent on n)
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FORMULA
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a(n) = A055229(n)^3 = g^3 = ggg; n = (KK)*(ggg)*f = K^2*g^3*f = KK*a(n)^3*f
Multiplicative with a(p^e)=1 for even e, a(p)=1, a(p^e)=p^3 for odd e>1. - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 01 2002
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EXAMPLE
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If n=24, largest square divisor is 4, square-free part is 6, g=2, a(24)=8; n=81, largest square divisor is 81, both F and g is 1, a(81)=1.
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CROSSREFS
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Cf. A055229, A000188, A008833, A007913, A055231, A056192.
Sequence in context: A095893 A095886 A076346 this_sequence A103760 A008834 A056201
Adjacent sequences: A056188 A056189 A056190 this_sequence A056192 A056193 A056194
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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 02 2000
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