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A088077
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a(n) is the least number m sandwiched between m-1 and m+1, both with special properties as follows: both are squarefree; both have n distinct prime factors.
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2
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4, 34, 664, 18446, 887314, 84946016, 3086525014, 557027507464, 31110090768184, 3404401335645584, 609352762511672906
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OFFSET
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1,1
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COMMENTS
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a(n) is surely larger than the n-th, but seems even larger than the (n+1)-th primorial number.
a(n) is neither necessarily squarefree nor it has a specified number of distinct prime-factors.
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LINKS
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Table of n, a(n) for n=1..11.
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EXAMPLE
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a(3) = 664, 663 = 3*13*17 and 665 = 5*11*19 both have three prime divisors.
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MATHEMATICA
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lf[x_] := Length[FactorInteger[x]] am[x_] := Abs[MoebiusMu[x]] q[x_] := Apply[Times, Table[Prime[j], {j, 1, x}]] Table[flag=1; Print["#"]; Do[s1=am[n-1]; s2=am[n+1]; If[Equal[s1, 1]&&Equal[s2, 1]&&Equal[lf[n-1], j] &&Equal[lf[n+1], j]&&Equal[flag, 1], Print[{n, j}]; flag=0], {n, q[j], q[j]+...}], {j, 1, 4}]
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CROSSREFS
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Cf. A002110, A001221.
Sequence in context: A030243 A222789 A326206 * A162079 A353041 A113231
Adjacent sequences: A088074 A088075 A088076 * A088078 A088079 A088080
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KEYWORD
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nonn,hard,more,changed
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AUTHOR
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Amarnath Murthy, Sep 22 2003
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EXTENSIONS
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Edited by Labos Elemer, Sep 26 2003
84946016 from Ray Chandler, Oct 09 2003
a(7) and a(8) from Donovan Johnson, Apr 22 2008
a(9)-a(11) from Donovan Johnson, Feb 18 2009
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STATUS
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approved
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