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%I #5 Nov 18 2019 16:42:26
%S 1,2,2,3,2,2,2,4,3,4,2,2,2,4,2,5,2,6,2,2,4,4,2,2,3,4,4,2,2,8,2,6,4,4,
%T 2,3,2,4,4,4,2,8,2,2,2,4,2,2,3,6,4,2,2,4,4,8,4,4,2,6,2,4,2,7,4,8,2,2,
%U 4,8,2,6,2,4,6,2,2,8,2,2,5,4,2,12,4,4,4,8,2,4,4,2,4,4,4,2,2,6,2,9,2,8,2,8,8
%N a(n) = gcd(d(n), d(A108951(n))), where d(n) gives the number of divisors of n, A000005(n), and A108951 is fully multiplicative with a(prime(i)) = prime(i)# = prime(1) * ... * prime(i).
%H Antti Karttunen, <a href="/A329612/b329612.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/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F a(n) = gcd(A000005(n),A329605(n)) = gcd(A000005(n),A000005(A108951(n))).
%o (PARI)
%o A034386(n) = prod(i=1, primepi(n), prime(i));
%o A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
%o A329612(n) = gcd(numdiv(n),numdiv(A108951(n)));
%Y Cf. A000005, A034386, A108951, A329614.
%K nonn
%O 1,2
%A _Antti Karttunen_, Nov 18 2019
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