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A324189 a(n) = A324122(A163511(n)).

%I A324189 #6 Feb 19 2019 00:11:06
%S A324189 0,2,6,2,14,12,0,4,30,36,36,30,24,12,16,6,60,120,96,152,90,122,90,54,
%T A324189 48,72,48,44,36,28,16,10,126,362,360,780,272,600,464,396,192,402,360,
%U A324189 336,216,222,168,132,120,120,216,246,144,168,128,92,80,102,48,68,0,36,32,12,254,1092,1080,3900,846,3122,2342,2800,576,2016,1824,2360,1080
%N A324189 a(n) = A324122(A163511(n)).
%H A324189 Antti Karttunen, <a href="/A324189/b324189.txt">Table of n, a(n) for n = 0..16383</a>
%H A324189 Antti Karttunen, <a href="/A324189/a324189.txt">Data supplement: n, a(n) computed for n = 0..65537</a>
%F A324189 a(n) = A324184(n) - A324188(n) = A324184(n) - gcd(A324184(n),A163511(n)*A324183(n)).
%o A324189 (PARI)
%o A324189 A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A324189 A324122(n) = (sigma(n) - gcd(sigma(n),n*numdiv(n)));
%o A324189 A324189(n) = A324122(A163511(n));
%o A324189 (PARI)
%o A324189 A324183(n) = if(!n,1,n = ((3<<#binary(n\2))-n-1); my(e=0,m=1); while(n>0, if(!(n%2), m *= (1+e); e=0, e++); n >>= 1); (m*(1+e)));
%o A324189 A324184(n) = if(!n,1,my(p=2,mp=p*p,m=1); while(n>1, if(n%2, p=nextprime(1+p); mp = p*p, if((2==n)||!(n%4),mp *= p,m *= (mp-1)/(p-1))); n >>= 1); (m*(mp-1)/(p-1)));
%o A324189 A324189(n) = (A324184(n) - gcd(A324184(n), A163511(n)*A324183(n)));
%Y A324189 Cf. A163511, A324183, A324184, A324188.
%Y A324189 Cf. A324199 (positions of zeros).
%K A324189 nonn
%O A324189 0,2
%A A324189 _Antti Karttunen_, Feb 17 2019