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A342915 a(n) = gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).

%I A342915 #14 Dec 22 2021 10:30:28
%S A342915 1,3,4,1,6,1,8,3,2,1,12,1,14,3,8,1,18,1,20,3,2,1,24,1,2,3,4,1,30,1,32,
%T A342915 3,2,1,12,1,38,3,8,1,42,1,44,9,2,1,48,1,2,3,4,1,54,1,8,3,2,1,60,1,62,
%U A342915 3,32,1,6,1,68,3,2,1,72,1,74,3,4,1,6,1,80,9,2,1,84,1,2,3,8,1,90,1,4,3,2,1,24,1,98,3,4,1,102
%N A342915 a(n) = gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).
%H A342915 Antti Karttunen, <a href="/A342915/b342915.txt">Table of n, a(n) for n = 1..16384</a>
%F A342915 a(n) = gcd(1+n, A001615(n)).
%F A342915 a(n) = (1+n) / A342916(n) = A001615(n) / A342917(n).
%t A342915 psi[n_] := If[n==1, 1, Times @@ ((#1+1)*#1^(#2-1)& @@@ FactorInteger[n])];
%t A342915 a[n_] := GCD[n+1, psi[n]];
%t A342915 Array[a, 105] (* _Jean-François Alcover_, Dec 22 2021 *)
%o A342915 (PARI)
%o A342915 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 A342915 A342915(n) = gcd(1+n,A001615(n));
%Y A342915 Cf. A001615, A342916, A342917.
%Y A342915 Cf. also A049559, A342458.
%Y A342915 After n=1 differs from A143771 for the first time at n=44, where a(44) = 9, while A143771(44) = 3.
%K A342915 nonn
%O A342915 1,2
%A A342915 _Antti Karttunen_, Mar 29 2021