cp's OEIS Frontend

A152443 a(n) = the largest proper divisor of n that is coprime to d(n), where d(n) = the number of divisors of n.

%I A152443 #14 Jun 24 2025 00:52:40
%S A152443 1,1,2,1,3,1,1,1,5,1,1,1,7,5,8,1,1,1,5,7,11,1,3,5,13,9,7,1,15,1,1,11,
%T A152443 17,7,4,1,19,13,5,1,21,1,11,5,23,1,3,7,25,17,13,1,27,11,7,19,29,1,5,1,
%U A152443 31,7,32,13,33,1,17,23,35,1,1,1,37,25,19,11,39,1,1,27,41,1,7,17,43,29,11,1,5
%N A152443 a(n) = the largest proper divisor of n that is coprime to d(n), where d(n) = the number of divisors of n.
%C A152443 If n is squarefree then a(n) = A032742(n). - _Robert Israel_, Jun 23 2025
%H A152443 Robert Israel, <a href="/A152443/b152443.txt">Table of n, a(n) for n = 2..10000</a>
%e A152443 There are 4 divisors of 27. These are 1,3,9,27. The proper divisors of 27 are therefore 1,3,9. The largest of these that is coprime to d(27) = 4 is 9. So a(27) = 9. (Note that in this case, the largest divisor of 27 coprime to 4 is 27, not 9.)
%p A152443 f:= proc(n) local d,D;
%p A152443    D:= numtheory:-divisors(n);
%p A152443    d:= nops(D);
%p A152443    max(select(t -> igcd(d,t)=1, D minus {n}))
%p A152443 end proc:
%p A152443 map(f, [$2..100]); # _Robert Israel_, Jun 23 2025
%t A152443 Table[Max[Select[Drop[Divisors[n], -1], GCD[DivisorSigma[0, n], # ] == 1 &]], {n, 2, 100}] (* _Stefan Steinerberger_, Dec 06 2008 *)
%Y A152443 Cf. A000005, A032742, A137926, A152444.
%K A152443 nonn,look
%O A152443 2,3
%A A152443 _Leroy Quet_, Dec 04 2008
%E A152443 Extended by _Ray Chandler_ and _Stefan Steinerberger_, Dec 05 2008