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A328098 If A327928(n) is zero, a(n) = A003415(n), otherwise a(n) = A327858(n) = gcd(A003415(n), A276086(n)).

%I A328098 #7 Oct 08 2019 16:25:58
%S A328098 0,1,1,1,1,5,1,1,6,7,1,1,1,9,1,1,1,21,1,1,10,13,1,1,10,15,3,1,1,31,1,
%T A328098 5,14,19,1,1,1,21,1,1,1,41,1,1,39,25,1,7,14,45,5,7,1,3,1,1,22,31,1,1,
%U A328098 1,33,51,1,18,61,1,1,26,59,1,1,1,39,55,5,18,71,1,1,1,43,1,1,22,45,1,35,1,123,5,1,34,49,1,1,1,77,75,35,1,91,1,1,71
%N A328098 If A327928(n) is zero, a(n) = A003415(n), otherwise a(n) = A327858(n) = gcd(A003415(n), A276086(n)).
%C A328098 After zero, sequence contains only terms of A048103.
%H A328098 Antti Karttunen, <a href="/A328098/b328098.txt">Table of n, a(n) for n = 1..65537</a>
%o A328098 (PARI)
%o A328098 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328098 A129251(n) = { my(f = factor(n)); sum(k=1, #f~, (f[k, 2]>=f[k, 1])); };
%o A328098 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 A328098 A328098(n) = if(1==n,0,my(u=A003415(n)); if(!A129251(u),u,gcd(u,A276086(u))));
%Y A328098 Cf. A003415, A048103, A129251, A276085, A276086, A327858, A327859, A327928, A327929, A327963, A327965, A328097, A328099.
%K A328098 nonn
%O A328098 1,6
%A A328098 _Antti Karttunen_, Oct 07 2019