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%I #20 Dec 21 2023 10:24:23
%S 4,3,8,9,2,1,2,15,16,9,20,7,22,3,1,13,27,7,30,1,11,17,35,1,38,3,40,3,
%T 44,1,46,3,49,25,51,13,54,55,56,57,58,5,62,63,64,65,66,17,69,7,8,37,
%U 75,19,7,39,80,81,82,7,85,43,29,11,18,91,92,93,94,19,96,49,99,25,34,13,15,53
%N a(n) = the largest divisor of A002808(n) that is coprime to n. (A002808(n) = the n-th composite.)
%C a(n) = A002808(n) for n in A073258. - _Robert Israel_, Dec 20 2023
%H Robert Israel, <a href="/A137924/b137924.txt">Table of n, a(n) for n = 1..10000</a>
%e The 12th composite is 21. The divisors of 21 are 1,3,7,21. The divisors of 21 that are coprime to 12 are 1 and 7. 7 is the largest of these; so a(12) = 7.
%p A002808 := proc(n) option remember ; local a; if n = 1 then 4; else for a from A002808(n-1)+1 do if not isprime(a) then RETURN(a) ; fi ; od: fi ; end: A137924 := proc(n) local dvs,d ; dvs := sort(convert(numtheory[divisors](A002808(n)),list),`>`) ; for d in dvs do if gcd(d,n) = 1 then RETURN(d) ; fi ; od: end: seq(A137924(n),n=1..80) ; # _R. J. Mathar_, Mar 03 2008
%t a = {}; c = 4; For[n = 1, n < 80, n++, AppendTo[a, Select[Divisors[c], GCD[ #, n] == 1 &][[ -1]]]; If[PrimeQ[c + 1], c = c + 2, c = c + 1]]; a (* _Stefan Steinerberger_, Mar 09 2008 *)
%Y Cf. A002808, A073258, A137925.
%K nonn,look
%O 1,1
%A _Leroy Quet_, Feb 23 2008
%E More terms from _R. J. Mathar_ and _Stefan Steinerberger_, Mar 03 2008
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