A306695 - OEIS

%I #28 Jun 09 2020 07:21:52

%S 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 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 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 a(n) = gcd(n, psi(n)).

%C Here psi(n) is Dedekind's psi function A001615.

%C a(n) <= n <= A001615(n).

%C a(n) = n iff a(n) * 2 = A001615(n), n > 1.

%C a(n) = 1 iff either n=2 or n is in A255602. - _Robert Israel_, Mar 12 2019

%H Robert Israel, <a href="/A306695/b306695.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dedekind_psi_function">Dedekind psi function</a>

%F a(n) = gcd(n, A001615(n)).

%p f:= proc(n) local p; igcd(n, n*mul(1+1/p, p=numtheory:-factorset(n))) end proc:

%p map(f, [$1..100]); # _Robert Israel_, Mar 11 2019

%t psi[n_] := If[n == 1, 1, n Times @@ (1 + 1/FactorInteger[n][[All, 1]])];

%t a[n_] := GCD[n, psi[n]];

%t Array[a, 100] (* _Jean-François Alcover_, Jun 08 2020 *)

%o (PARI) dpsi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615

%o a(n) = gcd(n, dpsi(n)); \\ _Michel Marcus_, Mar 05 2019

%Y Cf. A001615, A255602.

%K nonn

%O 1,4

%A _Torlach Rush_, Mar 05 2019