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%I #8 May 12 2022 16:13:09
%S 1,1,2,2,4,4,2,4,12,12,2,4,6,2,16,2,8,24,6,24,8,2,2,16,30,12,48,60,4,
%T 48,2,16,8,16,8,24,18,6,24,48,40,8,14,20,48,2,2,4,6,60,32,6,4,48,24,
%U 24,24,4,2,96,30,2,48,2,48,8,2,16,8,24,2,96,36,36,60,36,4,48,6,24,2,40,2,240,96,14,16,8,8,288
%N a(n) = gcd(A353749(n), A353750(n)), where A353749(n) = phi(n)*A064989(n), and A353750(n) = A353749(sigma(n)).
%H Antti Karttunen, <a href="/A353761/b353761.txt">Table of n, a(n) for n = 1..10000</a>
%H Antti Karttunen, <a href="/A353761/a353761.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = gcd(A353749(n), A353750(n)) = gcd(A353749(n), A353757(n)) = gcd(A353750(n), A353757(n)).
%F a(n) = A353749(n) / A353762(n) = A353750(n) / A353763(n).
%o (PARI)
%o A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o A353749(n) = (eulerphi(n)*A064989(n));
%o A353761(n) = { my(s=sigma(n)); gcd(A353749(s), A353749(n)); };
%Y Cf. A000010, A000203, A006872, A062401, A064989, A336549, A336550, A353757, A353762, A353763.
%K nonn
%O 1,3
%A _Antti Karttunen_, May 10 2022
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