%I #11 May 24 2017 14:31:03

%S 1,1,3,4,1,1,1,8,9,5,11,4,13,7,3,1,17,9,19,5,7,11,23,1,25,2,27,1,29,2,

%T 31,1,33,17,35,9,37,38,39,40,41,7,43,44,45,46,47,3,49,1,17,13,53,27,5,

%U 7,57,58,59,5,61,31,7,1,13,66,67,68,69,14,71,9,73,37,25,19,11,39,79,1,1

%N a(n) = the largest divisor of n that is coprime to A002808(n). (A002808(n) = the n-th composite.)

%H Harvey P. Dale, <a href="/A137925/b137925.txt">Table of n, a(n) for n = 1..1000</a>

%e The 12th composite is 21. The divisors of 12 are 1,2,3,4,6,12. The divisors of 12 that are coprime to 21 are 1,2,4. 4 is the largest of these, so a(12) = 4.

%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: A137925 := proc(n) local dvs,d,a002808 ; a002808 := A002808(n) ; dvs := sort(convert(numtheory[divisors](n),list),`>`) ; for d in dvs do if gcd(d,a002808) = 1 then RETURN(d) ; fi ; od: end: seq(A137925(n),n=1..120) ; # _R. J. Mathar_, Apr 17 2008

%t ldc[{n_,x_}]:=Module[{divs=Divisors[n]},Max[Select[divs,CoprimeQ[ #,x]&]]]; Module[{nn=120,c,len},c=Select[Range[nn],CompositeQ];len=Length[c];ldc/@Thread[{Range[len],c}]] (* _Harvey P. Dale_, May 24 2017 *)

%Y Cf. A137924.

%K nonn

%O 1,3

%A _Leroy Quet_, Feb 23 2008

%E More terms from _R. J. Mathar_, Apr 17 2008