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Search: id:A055231
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| A055231 |
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Write n = [K^2]*F where F is square-free, = [K^2]*g*f, where g = GCD[K^2,F] and f = F/g; then a(n) = f(n) = F(n)/g(n). Thus GCD[K^2,f] = 1. |
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24
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| 1, 2, 3, 1, 5, 6, 7, 1, 1, 10, 11, 3, 13, 14, 15, 1, 17, 2, 19, 5, 21, 22, 23, 3, 1, 26, 1, 7, 29, 30, 31, 1, 33, 34, 35, 1, 37, 38, 39, 5, 41, 42, 43, 11, 5, 46, 47, 3, 1, 2, 51, 13, 53, 2, 55, 7, 57, 58, 59, 15, 61, 62, 7, 1, 65, 66, 67, 17, 69, 70, 71, 1, 73, 74, 3, 19, 77, 78, 79, 5
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Differs from A007913; they coincide iff g(n) = 1.
a(n) is powerfree part of n, i.e. if n=Product(pi^ei) over all i [prime factorization) then a(n)=Product(pi^ei) over those i with ei=1; if n=b*c^2*d^3 then a(n) is minimum possible value of b - Henry Bottomley (se16(AT)btinternet.com), Sep 01 2000
Also denominator of n/sfk(n)^2, where sfk is the square-free kernel of n (A007947), numerator: A062378. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Dec 10 2002
Largest unitary square-free number dividing n (the unitary square-free kernel of n). - S. R. Finch (Steven.Finch(AT)inria.fr), Mar 01 2004
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
S. R. Finch, Unitarism and infinitarism.
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FORMULA
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a(n) = n/A057521(n)
Multiplicative with a(p)=p and a(p^e)=1 for e>1. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Nov 01 2001
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EXAMPLE
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If n = 15!, A008833(15!) = 30240*30240, A007913(15!) = 1430, g(15!) = 10, a(n) = A007913(15!) = 143 and GCD[30240,143] = 1. 15! = (30240*30240)*1430 = (30240^2)*10*143 = K*K*F = (K^2)*g*f
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CROSSREFS
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a(n) = A007913(n)/GCD[A008833(n!), A007913(n!)]
A008833, A007913, A000188.
Sequence in context: A114690 A049274 A130508 this_sequence A072400 A007913 A083346
Adjacent sequences: A055228 A055229 A055230 this_sequence A055232 A055233 A055234
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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), Jun 21 2000
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