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A081084
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Nonsquarefree numbers m such that rad(m+1)=rad(m)+1, where rad(m)=A007947(m) is the squarefree kernel of m.
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2
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8, 48, 224, 960, 65024, 261120, 1046528, 4190208, 268402688, 1073676288, 4294836224, 17179607040, 70368727400448, 4503599493152768, 18014398241046528, 72057593501057024, 288230375077969920
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OFFSET
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1,1
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COMMENTS
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For k >= 3, 2^k*(2^(k-2)-1) is in the sequence if and only if 2^(k-1)-1 and 2^(k-2)-1 are squarefree. So if m is a term, m+1=2^(k-1)-1 is a squarefree number squared. - Lambert Herrgesell (zero815(AT)googlemail.com), Feb 18 2007
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 48, p. 18, Ellipses, Paris 2008.
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LINKS
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EXAMPLE
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48 = 2^4*3 is in the sequence because it is not squarefree, its squarefree kernel is 6 and the squarefree kernel of 49 = 7^2 is 7.
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MAPLE
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with(numtheory): rad:=proc(n) local fs, c: fs:=convert(factorset(n), list): c:=nops(fs): product(fs[j], j=1..c) end: b:=proc(n) if mobius(n)=0 and rad(n+1)=rad(n)+1 then n else fi end:seq(b(n), n=1..1000); # Emeric Deutsch
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PROG
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(PARI) rad(n)=my(f=factor(n)[, 1]); prod(i=1, #f, f[i])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Edited and a(9) onwards supplied by Lambert Herrgesell (zero815(AT)googlemail.com), Feb 18 2007
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STATUS
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approved
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