A138308 a(1)=1. a(n) = smallest integer > a(n-1) that is coprime to n and is coprime to every (nonzero) exponent in the prime factorization of n.

1, 3, 4, 5, 6, 7, 8, 11, 13, 17, 18, 19, 20, 23, 26, 27, 28, 29, 30, 31, 32, 35, 36, 37, 39, 41, 43, 45, 46, 47, 48, 49, 50, 53, 54, 55, 56, 59, 61, 67, 68, 71, 72, 73, 77, 79, 80, 83, 85, 87, 88, 89, 90, 91, 92, 95, 97, 99, 100, 101, 102, 103, 107, 109, 111, 113, 114, 115, 116

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

8 has the prime-factorization of 2^3. The smallest integer > a(7)=8 that is coprime to both 8 and 3 is 11. (9 is not coprime to 3. 10 is not coprime to 8.) So a(8)=11.

Maple

A138308 := proc(n) option remember; local pfs, a, p, works ; if n = 1 then 1; else pfs := ifactors(n)[2] ; for a from procname(n-1)+1 do works := true ; if gcd(a, n) > 1 then works := false; else for p in pfs do if gcd(a, op(2, p)) > 1 then works := false; fi; end do ; end if; if works then return a; end if ; end do; end if; end: seq(A138308(n), n=1..120) ; # R. J. Mathar, Oct 24 2009

Mathematica

Fold[Append[#1, SelectFirst[Range[#1[[-1]] + 1, #1[[-1]] + 12], Function[k, AllTrue[Join[{#2}, FactorInteger[#2][[All, -1]] ], CoprimeQ[k, #] &]]]] &, {1}, Range[2, 69]] (* Michael De Vlieger, Oct 18 2017 *)

Crossrefs

Cf. A138309, A138310.

Sequence in context: A120561 A051016 A044951 * A039084 A277641 A085627

Adjacent sequences: A138305 A138306 A138307 * A138309 A138310 A138311

Keyword

nonn

Author

Leroy Quet, Mar 13 2008

Extensions

Extended beyond a(14) by R. J. Mathar, Oct 24 2009

Status

approved