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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 8 19:20 EDT 2020. Contains 335524 sequences. (Running on oeis4.)