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A327963 If A327928(n) > 0, a(n) = A276086(n), otherwise a(n) = A003415(n).

%I A327963 #18 Oct 08 2019 16:25:42
%S A327963 0,1,1,9,1,5,1,15,6,7,1,25,1,9,150,225,1,21,1,375,10,13,1,625,10,15,
%T A327963 3750,5625,1,31,1,21,14,19,126,35,1,21,210,315,1,41,1,525,39,25,1,875,
%U A327963 14,45,5250,7875,1,4375,8750,13125,22,31,1,49,1,33,51,441,18,61,1,735,26,59,1,1225,1,39,55,11025,18,71,1,18375,36750,43,1,30625,22,45
%N A327963 If A327928(n) > 0, a(n) = A276086(n), otherwise a(n) = A003415(n).
%C A327963 After zero, sequence contains only terms of A048103.
%H A327963 Antti Karttunen, <a href="/A327963/b327963.txt">Table of n, a(n) for n = 1..2310</a>
%H A327963 Antti Karttunen, <a href="/A327963/a327963.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A327963 If A327928(n) > 0 [when n is one of the terms in A327929], then a(n) = A276086(n), otherwise a(n) = A003415(n).
%F A327963 For n > 1, a(n) = A276086(A327964(n)).
%o A327963 (PARI)
%o A327963 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A327963 A129251(n) = { my(f = factor(n)); sum(k=1, #f~, (f[k, 2]>=f[k, 1])); };
%o A327963 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 A327963 A327963(n) = if(1==n,0,my(u=A003415(n)); if(!A129251(u),u,A276086(n)));
%Y A327963 Cf. A003415, A048103, A129251, A276085, A276086, A327859, A327928, A327929, A327964, A327965, A328097, A328098, A328099, A328113 (rgs-transform).
%Y A327963 Cf. also A285330.
%K A327963 nonn
%O A327963 1,4
%A A327963 _Antti Karttunen_, Oct 07 2019