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%I #8 May 19 2024 14:02:24
%S 1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,3,1,1,1,1,1,3,1,1,1,1,
%T 1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,3,1,1,1,1,1,3,1,1,
%U 1,1,1,3,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,3,1,1,1,1,1,3,1,1,1
%N a(n) is the greatest common divisor of n, sigma(n) and A003961(n), where A003961(n) is fully multiplicative function with a(prime(i)) = prime(i+1).
%H Antti Karttunen, <a href="/A372565/b372565.txt">Table of n, a(n) 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>
%o (PARI)
%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A372565(n) = gcd([n, sigma(n), A003961(n)]);
%Y Cf. A000203, A003961, A372566 (positions of terms > 1).
%Y Greatest common divisor of any two of the following: A009194, A322361, A342671.
%K nonn,easy
%O 1,6
%A _Antti Karttunen_, May 19 2024
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