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

Author

Leroy Quet, Oct 29 2007

Keywords

• nonn

Examples

			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.
		

Programs

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 *)

Formula

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

Extensions

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