cp's OEIS Frontend

A336316 The number of non-unitary divisors in the conjugated prime factorization of n: a(n) = A048105(A122111(n)).

%I A336316 #14 Jul 19 2020 02:17:43
%S A336316 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 A336316 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 A336316 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 A336316 The number of non-unitary divisors in the conjugated prime factorization of n: a(n) = A048105(A122111(n)).
%C A336316 Equally, the number of divisors in the conjugated prime factorization of n minus the number of its unitary divisors.
%C A336316 Note that A001221(A122111(n)) = A001221(n) for all n.
%H A336316 Antti Karttunen, <a href="/A336316/b336316.txt">Table of n, a(n) for n = 1..12000</a>
%H A336316 Antti Karttunen, <a href="/A336316/a336316.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A336316 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A336316 a(n) = A336315(n) - A034444(n) = A000005(A122111(n)) - 2^A001221(n).
%F A336316 a(n) = A048105(A122111(n)).
%o A336316 (PARI)
%o A336316 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 A336316(n) = (A336315(n)-(2^omega(n)));
%Y A336316 Cf. A000005, A001221, A034444, A048105, A122111, A286621, A336315.
%Y A336316 Cf. A055932 (the positions of zeros).
%K A336316 nonn
%O A336316 1,5
%A A336316 _Antti Karttunen_, Jul 18 2020