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A342916 a(n) = (1+n) / gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).

%I A342916 #14 May 31 2021 08:59:39
%S A342916 2,1,1,5,1,7,1,3,5,11,1,13,1,5,2,17,1,19,1,7,11,23,1,25,13,9,7,29,1,
%T A342916 31,1,11,17,35,3,37,1,13,5,41,1,43,1,5,23,47,1,49,25,17,13,53,1,55,7,
%U A342916 19,29,59,1,61,1,21,2,65,11,67,1,23,35,71,1,73,1,25,19,77,13,79,1,9,41,83,1,85,43,29,11,89,1,91,23,31
%N A342916 a(n) = (1+n) / gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).
%C A342916 It is conjectured that a(n) = 1 only when n is a prime, A000040. See _Thomas Ordowski_'s May 21 2017 problem in A001615.
%H A342916 Antti Karttunen, <a href="/A342916/b342916.txt">Table of n, a(n) for n = 1..16384</a>
%F A342916 a(n) = (1+n) / A342915(n) = (1+n) / gcd(1+n, A001615(n)).
%o A342916 (PARI)
%o A342916 A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
%o A342916 A342916(n) = ((1+n)/gcd(1+n,A001615(n)));
%Y A342916 Cf. A000040, A001615, A342915, A342917.
%Y A342916 Cf. also A160596.
%Y A342916 After n=1 differs from A342918 for the first time at n=44, where a(44) = 5, while A342918(44) = 15.
%K A342916 nonn
%O A342916 1,1
%A A342916 _Antti Karttunen_, Mar 29 2021
%E A342916 Incorrect A-number in the formula corrected by _Antti Karttunen_, May 31 2021