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

Author

Amarnath Murthy, Sep 22 2003

Keywords

• nonn
• hard
• more

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.

Examples

			a(3) = 664, 663 = 3*13*17 and 665 = 5*11*19 both have three prime divisors.
		

Crossrefs

Cf. A002110, A001221.

Programs

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}]

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