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A340089 a(n) = (n-1) / gcd(n-1, A091732(n)), where A091732 is an infinitary analog of Euler's phi function.

%I A340089 #5 Dec 31 2020 08:21:08
%S A340089 0,1,1,1,1,5,1,7,1,9,1,11,1,13,7,1,1,17,1,19,5,21,1,23,1,25,13,3,1,29,
%T A340089 1,31,8,33,17,35,1,37,19,13,1,41,1,43,11,45,1,47,1,49,25,17,1,53,27,
%U A340089 55,14,57,1,59,1,61,31,7,4,13,1,67,17,23,1,71,1,73,37,25,19,77,1,79,1,81,1,83,21,85,43,29,1,89
%N A340089 a(n) = (n-1) / gcd(n-1, A091732(n)), where A091732 is an infinitary analog of Euler's phi function.
%H A340089 Antti Karttunen, <a href="/A340089/b340089.txt">Table of n, a(n) for n = 1..65537</a>
%F A340089 a(n) = (n-1) / A340087(n) = (n-1) / gcd(n-1, A091732(n)).
%o A340089 (PARI)
%o A340089 ispow2(n) = (n && !bitand(n,n-1));
%o A340089 A302777(n) = ispow2(isprimepower(n));
%o A340089 A091732(n) = { my(m=1); while(n > 1, fordiv(n, d, if((d<n)&&A302777(n/d), m *= ((n/d)-1); n = d; break))); (m); };
%o A340089 A340089(n) = ((n-1)/gcd(n-1, A091732(n)));
%Y A340089 Cf. A091732, A340087, A340088.
%Y A340089 Cf. also A160596.
%K A340089 nonn
%O A340089 1,6
%A A340089 _Antti Karttunen_, Dec 31 2020