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a(n) = the largest divisor of n that is coprime to A000005(n). (A000005(n) = the number of positive divisors of n.)
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%I #16 Feb 12 2018 02:50:22

%S 1,1,3,4,5,3,7,1,1,5,11,1,13,7,15,16,17,1,19,5,21,11,23,3,25,13,27,7,

%T 29,15,31,1,33,17,35,4,37,19,39,5,41,21,43,11,5,23,47,3,49,25,51,13,

%U 53,27,55,7,57,29,59,5,61,31,7,64,65,33,67,17,69,35,71,1,73,37,25,19,77,39,79

%N a(n) = the largest divisor of n that is coprime to A000005(n). (A000005(n) = the number of positive divisors of n.)

%H Robert Israel, <a href="/A137926/b137926.txt">Table of n, a(n) for n = 1..10000</a>

%e 6 has 4 positive divisors. The divisors of 6 are 1,2,3,6. The divisors of 6 that are coprime to 4 are 1 and 3. 3 is the largest of these; so a(6) = 3.

%p f := proc (n) local D, t; D := numtheory:-divisors(n); t := nops(D); max(select(proc (d) options operator, arrow; igcd(d, t) = 1 end proc, D)) end proc:

%p map(f, [$1..100]); # _Robert Israel_, Feb 11 2018

%t Table[Select[Divisors[n], GCD[ #, Length[Divisors[n]]] == 1 &][[ -1]], {n, 1, 80}] (* _Stefan Steinerberger_, Mar 09 2008 *)

%o (PARI) a(n) = {my(d = divisors(n)); vecmax(select(x->(gcd(x, #d) == 1), d));} \\ _Michel Marcus_, Feb 12 2018

%Y Cf. A046642 (a(n)=n), A120737 (a(n)=1), A137927.

%K nonn

%O 1,3

%A _Leroy Quet_, Feb 23 2008

%E More terms from _Stefan Steinerberger_, Mar 09 2008