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A264024 a(n) = gcd(phi(k), k-1) / lambda(k), where k is n-th Carmichael number A002997(n) and lambda(k) = A002322(k).

%I A264024 #21 Apr 21 2024 09:59:26
%S A264024 1,1,12,2,1,1,9,1,4,1,6,18,1,1,1,2,1,1,1,2,12,1,1,1,1,3,3,3,50,1,18,2,
%T A264024 1,2,1,2,5,36,1,1,2,3,4,3,3,2,3,1,1,3,3,2,4,2,5,1,4,4,4,1,1,3,40,28,1,
%U A264024 2,4,2,4,1,2,1,2,1,33,5,50,64,1,1,3,2,1,1,12,3,1,12,1,1,1,24,1,3,128,1,6,8,5,20,3,2,2,6,4
%N A264024 a(n) = gcd(phi(k), k-1) / lambda(k), where k is n-th Carmichael number A002997(n) and lambda(k) = A002322(k).
%H A264024 Amiram Eldar, <a href="/A264024/b264024.txt">Table of n, a(n) for n = 1..10000</a>
%F A264024 a(n) = A049559(k)/A002322(k), where k = A002997(n).
%t A264024 t = Cases[Range[1, 16 (10^6), 2], n_ /; Mod[n, CarmichaelLambda@ n] == 1 && ! PrimeQ@ n]; Table[GCD[EulerPhi@ t[[n]], t[[n]] - 1]/CarmichaelLambda@ t[[n]], {n, 105}] (* _Michael De Vlieger_, Nov 03 2015, after _Artur Jasinski_ at A002997: alternatively use A002997 data for t *)
%o A264024 (PARI) t(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1;
%o A264024 is(n)=n%2 && !isprime(n) && t(n) && n>1;
%o A264024 c(n)=gcd(eulerphi(n),n-1)/lcm(znstar(n)[2]);
%o A264024 for(n=1, 1e7, if(is(n), print1(c(n)", "))) \\ _Altug Alkan_, Nov 01 2015
%Y A264024 Cf. A002322, A002997, A049559, A174590, A264012.
%K A264024 nonn
%O A264024 1,3
%A A264024 _Thomas Ordowski_, Nov 01 2015
%E A264024 More terms from _Altug Alkan_, Nov 01 2015