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.

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.

Links

Table of n, a(n) for n=1..11.

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

Cf. A002110, A001221.

Sequence in context: A030243 A222789 A326206 * A358326 A162079 A353041

Adjacent sequences: A088074 A088075 A088076 * A088078 A088079 A088080

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