cp's OEIS Frontend

A340079 a(n) = n / gcd(n, 1+A018804(n)), where A018804(n) = Sum_{k=1..n} gcd(k, n).

%I A340079 #8 Dec 31 2020 08:20:38
%S A340079 1,1,1,4,1,3,1,8,9,5,1,12,1,7,15,16,1,9,1,20,7,11,1,24,25,13,27,4,1,
%T A340079 15,1,32,33,17,35,36,1,19,13,40,1,3,1,44,9,23,1,48,49,25,51,52,1,27,
%U A340079 11,56,19,29,1,60,1,31,63,64,65,33,1,68,69,35,1,72,1,37,75,76,77,39,1,80,81,41,1,84,85,43,87,88
%N A340079 a(n) = n / gcd(n, 1+A018804(n)), where A018804(n) = Sum_{k=1..n} gcd(k, n).
%C A340079 It is conjectured that this is 1 iff n is 1 or a prime. See _Thomas Ordowski_'s Oct 22 2014 comment in A018804.
%H A340079 Antti Karttunen, <a href="/A340079/b340079.txt">Table of n, a(n) for n = 1..8191</a>
%H A340079 Antti Karttunen, <a href="/A340079/a340079.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A340079 a(n) = n / A340078(n) = n / gcd(n, 1+A018804(n)).
%o A340079 (PARI)
%o A340079 A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804
%o A340079 A340079(n) = (n/gcd(n,1+A018804(n)));
%Y A340079 Cf. A018804, A340078, A340080.
%Y A340079 Cf. also A055032, A323072 (similar but different sequences).
%K A340079 nonn
%O A340079 1,4
%A A340079 _Antti Karttunen_, Dec 30 2020