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A342416 a(n) = gcd(A173557(n), A342001(n)).

%I A342416 #11 Mar 12 2021 23:13:49
%S A342416 1,1,1,1,1,1,1,1,2,1,1,2,1,3,8,1,1,1,1,4,2,1,1,1,2,3,1,2,1,1,1,1,2,1,
%T A342416 12,2,1,3,8,1,1,1,1,2,1,1,1,2,2,1,4,4,1,1,8,1,2,1,1,2,1,3,1,1,6,1,1,4,
%U A342416 2,1,1,1,1,3,1,2,6,1,1,2,2,1,1,2,2,3,8,5,1,1,4,2,2,1,24,1,1,1,5,2,1,1,1,1,1
%N A342416 a(n) = gcd(A173557(n), A342001(n)).
%H A342416 Antti Karttunen, <a href="/A342416/b342416.txt">Table of n, a(n) for n = 1..65537</a>
%F A342416 a(n) = A342413(n) / A003557(n) = gcd(A173557(n), A342001(n)).
%t A342416 Array[GCD[#2, #1/#3] & @@ {If[#1 < 2, 0, #1 Total[#2/#1 & @@@ #2]], If[#1 == 1, 1, Times @@ Map[# - 1 &, #2[[All, 1]] ]], #1/Times @@ #2[[All, 1]]} & @@ {Abs[#], FactorInteger[#]} &, 91] (* _Michael De Vlieger_, Mar 11 2021 *)
%o A342416 (PARI)
%o A342416 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A342416 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A342416 A342413(n) = gcd(eulerphi(n), A003415(n));
%o A342416 A342416(n) = (A342413(n)/A003557(n));
%Y A342416 Cf. A000010, A003415, A003557, A173557, A342001, A342413.
%K A342416 nonn
%O A342416 1,9
%A A342416 _Antti Karttunen_, Mar 11 2021