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A327964 a(1) = 1, and for n > 1, a(n) = A276085(A327963(n)).

%I A327964 #11 Oct 14 2019 13:52:05
%S A327964 1,0,0,4,0,6,0,8,3,30,0,12,0,4,15,16,0,32,0,20,7,2310,0,24,7,8,27,28,
%T A327964 0,6469693230,0,32,31,510510,35,36,0,32,39,40,0,7420738134810,0,44,
%U A327964 2312,12,0,48,31,10,51,52,0,54,55,56,211,6469693230,0,60,0,212,30032,64,5,1922760350154212639070,0,68,2311,32589158477190044730,0,72,0,2312,216,76,5
%N A327964 a(1) = 1, and for n > 1, a(n) = A276085(A327963(n)).
%H A327964 Antti Karttunen, <a href="/A327964/b327964.txt">Table of n, a(n) for n = 1..2048</a>
%F A327964 a(1) = 1, and for n > 1, a(n) = A276085(A327963(n)).
%F A327964 a(p) = 0 for all primes p.
%F A327964 a(A327929(n)) = A327929(n) for all n. [But note that there are also other fixed points.]
%o A327964 (PARI)
%o A327964 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A327964 A129251(n) = { my(f = factor(n)); sum(k=1, #f~, (f[k, 2]>=f[k, 1])); };
%o A327964 A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
%o A327964 A327963(n) = if(1==n,0,my(u=A003415(n)); if(!A129251(u),u,A276086(n)));
%o A327964 A002110(n) = prod(i=1,n,prime(i));
%o A327964 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
%o A327964 A327964(n) = if(1==n,n,A276085(A327963(n)));
%Y A327964 Cf. A002110, A003415, A129251, A276085, A276086, A327963, A328113.
%Y A327964 Cf. A327929 (a subsequence of fixed points).
%K A327964 nonn
%O A327964 1,4
%A A327964 _Antti Karttunen_, Oct 07 2019