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A303781 a(2) = 1; for n <> 2, a(n) = gcd(n, A000005(n)), where A000005(n) = number of divisors of n.

%I A303781 #7 Mar 20 2023 10:05:08
%S A303781 1,1,1,1,1,2,1,4,3,2,1,6,1,2,1,1,1,6,1,2,1,2,1,8,1,2,1,2,1,2,1,2,1,2,
%T A303781 1,9,1,2,1,8,1,2,1,2,3,2,1,2,1,2,1,2,1,2,1,8,1,2,1,12,1,2,3,1,1,2,1,2,
%U A303781 1,2,1,12,1,2,3,2,1,2,1,10,1,2,1,12,1,2,1,8,1,6,1,2,1,2,1,12,1,2,3,1,1,2,1,8,1
%N A303781 a(2) = 1; for n <> 2, a(n) = gcd(n, A000005(n)), where A000005(n) = number of divisors of n.
%C A303781 Except for a(2) = 1, a(n) = A009191(n).
%H A303781 Antti Karttunen, <a href="/A303781/b303781.txt">Table of n, a(n) for n = 1..65537</a>
%F A303781 a(2) = 1; for n <> 2, a(n) = gcd(n, A000005(n)).
%t A303781 Join[{1,1},Table[GCD[n,DivisorSigma[0,n]],{n,3,110}]] (* _Harvey P. Dale_, Mar 20 2023 *)
%o A303781 (PARI) A303781(n) = if(2==n,1,gcd(n,numdiv(n)));
%Y A303781 Cf. A000005, A009191.
%K A303781 nonn
%O A303781 1,6
%A A303781 _Antti Karttunen_, Apr 30 2018