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A306695 a(n) = gcd(n, psi(n)).

%I A306695 #28 Jun 09 2020 07:21:52
%S A306695 1,1,1,2,1,6,1,4,3,2,1,12,1,2,3,8,1,18,1,4,1,2,1,24,5,2,9,4,1,6,1,16,
%T A306695 3,2,1,36,1,2,1,8,1,6,1,4,9,2,1,48,7,10,3,4,1,54,1,8,1,2,1,12,1,2,3,
%U A306695 32,1,6,1,4,3,2,1,72,1,2,15,4,1,6,1,16,27,2,1,12,1,2,3,8,1,18,7,4,1,2,5,96,1,14,9,20
%N A306695 a(n) = gcd(n, psi(n)).
%C A306695 Here psi(n) is Dedekind's psi function A001615.
%C A306695 a(n) <= n <= A001615(n).
%C A306695 a(n) = n iff a(n) * 2 = A001615(n), n > 1.
%C A306695 a(n) = 1 iff either n=2 or n is in A255602. - _Robert Israel_, Mar 12 2019
%H A306695 Robert Israel, <a href="/A306695/b306695.txt">Table of n, a(n) for n = 1..10000</a>
%H A306695 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dedekind_psi_function">Dedekind psi function</a>
%F A306695 a(n) = gcd(n, A001615(n)).
%p A306695 f:= proc(n) local p; igcd(n, n*mul(1+1/p, p=numtheory:-factorset(n))) end proc:
%p A306695 map(f, [$1..100]); # _Robert Israel_, Mar 11 2019
%t A306695 psi[n_] := If[n == 1, 1, n Times @@ (1 + 1/FactorInteger[n][[All, 1]])];
%t A306695 a[n_] := GCD[n, psi[n]];
%t A306695 Array[a, 100] (* _Jean-François Alcover_, Jun 08 2020 *)
%o A306695 (PARI) dpsi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615
%o A306695 a(n) = gcd(n, dpsi(n)); \\ _Michel Marcus_, Mar 05 2019
%Y A306695 Cf. A001615, A255602.
%K A306695 nonn
%O A306695 1,4
%A A306695 _Torlach Rush_, Mar 05 2019