A132009 a(1) = 1; for n>=2, a(n) = n-th positive integer which is coprime to the largest prime divisor of n.

1, 3, 4, 7, 6, 8, 8, 15, 13, 12, 12, 17, 14, 16, 18, 31, 18, 26, 20, 24, 24, 24, 24, 35, 31, 28, 40, 32, 30, 37, 32, 63, 36, 36, 40, 53, 38, 40, 42, 49, 42, 48, 44, 48, 56, 48, 48, 71, 57, 62, 54, 56, 54, 80, 60, 65, 60, 60, 60, 74, 62, 64, 73, 127, 70, 72, 68, 72, 72, 81, 72, 107

Offset

1,2

Links

Table of n, a(n) for n=1..72.

Formula

a(n)=A126572(A006530(n),n). - R. J. Mathar, Nov 09 2007

Example

The largest prime dividing 12 is 3. The positive integers which are coprime to 3 are 1,2,4,5,7,8,10,11,13,14,16,17,19,20,... The 12th of these is 17, so a(12) = 17.

Maple

A126572 := proc(n, k) local f, i ; f := 1 ; for i from 1 do if gcd(i, n) = 1 then if f = k then RETURN(i) ; fi ; f := f+1 ; fi ; od: end: A006530 := proc(n) if n = 1 then 1; else max(seq(op(1, i), i=ifactors(n)[2]) ) ; fi ; end: A132009 := proc(n) local p ; p := A006530(n) ; A126572(p, n) ; end: seq(A132009(n), n=1..100) ; # R. J. Mathar, Nov 09 2007

Mathematica

a = {1}; For[n = 2, n < 70, n++, b = FactorInteger[n][[ -1, 1]]; c = 0; i = 1; While[c < n, If[GCD[i, b] == 1, c++ ]; i++ ]; AppendTo[a, i - 1]]; a (* Stefan Steinerberger, Nov 04 2007 *)

Crossrefs

Sequence in context: A120224 A210471 A183107 * A295565 A086455 A204823

Adjacent sequences: A132006 A132007 A132008 * A132010 A132011 A132012

Keyword

nonn

Author

Leroy Quet, Oct 29 2007

Extensions

More terms from Stefan Steinerberger and R. J. Mathar, Nov 04 2007

Status

approved