A071255 a(1) = 2, a(n+1) = a(n)-th squarefree number > 1.

2, 3, 5, 7, 11, 17, 29, 46, 74, 119, 195, 319, 521, 859, 1407, 2315, 3810, 6267, 10303, 16942, 27862, 45822, 75381, 123998, 203969, 335507, 551886, 907818, 1493294, 2456374, 4040526, 6646389, 10932823, 17983831, 29582198, 48660745, 80043762

Offset: 1

Author

Amarnath Murthy, May 22 2002

Keywords

• nonn

Comments

Here 1 is not considered a squarefree number.

Examples

			a(2) = 3 and the third squarefree number is 5 hence a(3) = 5.
a(4) = 7 hence a(5) = 11 is the 7th squarefree number (2,3,5,6,7,10,11...)
75381 is the 45822nd squarefree number.
		

Links

• Daniel Suteu, Table of n, a(n) for n = 1..90

Crossrefs

Cf. A005117, A013661.

Programs

Mathematica

sqf = {}; Do[ If[ SquareFreeQ[n], sqf = Append[sqf, n]], {n, 2, 334000} ]; a[1] = 2; a[n_] := sqf[[ a[n - 1]]]; Table[ a[n], {n, 1, 26}]
a[1]=2; a[x_] := Part[t, a[x-1]] t=Flatten[Position[Table[Abs[MoebiusMu[w]], {w, 2, 35000}], 1]]+1; t1=Table[a[w], {w, 1, 21}]

Formula

a(n) = A005117(a(n-1)+1), a(1) = 2.

Limit_{n->infinity} a(n+1)/a(n) = zeta(2). - Daniel Suteu, Jul 07 2022

Extensions

More terms from Robert G. Wilson v and Labos Elemer, Jun 07 2002

a(27)-a(37) from Donovan Johnson, Oct 29 2010