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A328097 If A327928(n) is zero, a(n) = A003415(n), otherwise a(n) = A327859(n) = A276086(A003415(n)).

%I A328097 #12 Oct 08 2019 16:25:50
%S A328097 0,1,1,9,1,5,1,25,6,7,1,225,1,9,15,21,1,21,1,625,10,13,1,525,10,15,
%T A328097 3750,21,1,31,1,18375,14,19,25,49,1,21,225,735,1,41,1,875,39,25,1,
%U A328097 385875,14,45,375,13125,1,36750,225,1029,22,31,1,1029,1,33,51,2941225,18,61,1,1225,26,59,1,84035,1,39,55,18375,18,71,1,31513125,42875
%N A328097 If A327928(n) is zero, a(n) = A003415(n), otherwise a(n) = A327859(n) = A276086(A003415(n)).
%C A328097 After zero, sequence contains only terms of A048103.
%C A328097 Note that there are fixed points, like a(15) = 15.
%H A328097 Antti Karttunen, <a href="/A328097/b328097.txt">Table of n, a(n) for n = 1..1728</a>
%H A328097 Antti Karttunen, <a href="/A328097/a328097.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%o A328097 (PARI)
%o A328097 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328097 A129251(n) = { my(f = factor(n)); sum(k=1, #f~, (f[k, 2]>=f[k, 1])); };
%o A328097 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 A328097 A328097(n) = if(1==n,0,my(u=A003415(n)); if(!A129251(u),u,A276086(u)));
%Y A328097 Cf. A003415, A048103, A129251, A276085, A276086, A327859, A327928, A327929, A327963, A327965, A328098, A328099.
%K A328097 nonn
%O A328097 1,4
%A A328097 _Antti Karttunen_, Oct 07 2019