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A088077
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.
2
4, 34, 664, 18446, 887314, 84946016, 3086525014, 557027507464, 31110090768184, 3404401335645584, 609352762511672906
OFFSET
1,1
COMMENTS
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.
EXAMPLE
a(3) = 664, 663 = 3*13*17 and 665 = 5*11*19 both have three prime divisors.
MATHEMATICA
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}]
CROSSREFS
Sequence in context: A030243 A222789 A326206 * A358326 A162079 A353041
KEYWORD
nonn,hard,more
AUTHOR
Amarnath Murthy, Sep 22 2003
EXTENSIONS
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
STATUS
approved