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The number of divisors in the conjugated prime factorization of n: a(n) = A000005(A122111(n)).
4

%I #11 Jul 19 2020 02:17:24

%S 1,2,3,2,4,4,5,2,3,6,6,4,7,8,6,2,8,4,9,6,9,10,10,4,4,12,3,8,11,8,12,2,

%T 12,14,8,4,13,16,15,6,14,12,15,10,6,18,16,4,5,6,18,12,17,4,12,8,21,20,

%U 18,8,19,22,9,2,16,16,20,14,24,12,21,4,22,24,6,16,10,20,23,6,3,26,24,12,20,28,27,10,25,8,15,18,30,30,24

%N The number of divisors in the conjugated prime factorization of n: a(n) = A000005(A122111(n)).

%H Antti Karttunen, <a href="/A336315/b336315.txt">Table of n, a(n) for n = 1..12000</a>

%H Antti Karttunen, <a href="/A336315/a336315.txt">Data supplement: n, a(n) computed for n = 1..65539</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A000005(A122111(n)).

%F a(n) = A336316(n) + A034444(n).

%o (PARI) A336315(n) = if(1==n,n,my(p=apply(primepi,factor(n)[,1]~),m=1+p[1]); for(i=2, #p, m *= (1+p[i]-p[i-1])); (m));

%Y Cf. A000005, A034444, A122111, A286621, A323173, A322813, A322819, A336316.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 18 2020