Search: id:A138308
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%I A138308
%S A138308 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,
%T A138308 43,45,46,47,48,49,50,53,54,55,56,59,61,67,68,71,72,73,77,79,80,83,85,
%U A138308 87,88,89,90,91,92,95,97,99,100,101,102,103,107,109,111,113,114,115,116
%N 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.
%H A138308 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A138308 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.
%p A138308 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) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 
               24 2009]
%Y A138308 Cf. A138309, A138310.
%Y A138308 Sequence in context: A120561 A051016 A044951 this_sequence A039084 A085627 
               A057825
%Y A138308 Adjacent sequences: A138305 A138306 A138307 this_sequence A138309 A138310 
               A138311
%K A138308 nonn
%O A138308 1,2
%A A138308 Leroy Quet Mar 13 2008
%E A138308 Extended beyond a(14) by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 24 2009

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