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The number of non-unitary divisors in the conjugated prime factorization of n: a(n) = A048105(A122111(n)).
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%I #14 Jul 19 2020 02:17:43

%S 0,0,1,0,2,0,3,0,1,2,4,0,5,4,2,0,6,0,7,2,5,6,8,0,2,8,1,4,9,0,10,0,8,

%T 10,4,0,11,12,11,2,12,4,13,6,2,14,14,0,3,2,14,8,15,0,8,4,17,16,16,0,

%U 17,18,5,0,12,8,18,10,20,4,19,0,20,20,2,12,6,12,21,2,1,22,22,4,16,24,23,6,23,0,11,14,26,26,20,0,24

%N The number of non-unitary divisors in the conjugated prime factorization of n: a(n) = A048105(A122111(n)).

%C Equally, the number of divisors in the conjugated prime factorization of n minus the number of its unitary divisors.

%C Note that A001221(A122111(n)) = A001221(n) for all n.

%H Antti Karttunen, <a href="/A336316/b336316.txt">Table of n, a(n) for n = 1..12000</a>

%H Antti Karttunen, <a href="/A336316/a336316.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>

%F a(n) = A336315(n) - A034444(n) = A000005(A122111(n)) - 2^A001221(n).

%F a(n) = A048105(A122111(n)).

%o (PARI)

%o 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));

%o A336316(n) = (A336315(n)-(2^omega(n)));

%Y Cf. A000005, A001221, A034444, A048105, A122111, A286621, A336315.

%Y Cf. A055932 (the positions of zeros).

%K nonn

%O 1,5

%A _Antti Karttunen_, Jul 18 2020