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A328112 a(1) = 0, for primes p, a(p) = 1, and for any other number n, a(n) = max(A003415(n), A276086(n)).

%I A328112 #9 Oct 08 2019 16:26:23
%S A328112 0,1,1,9,1,5,1,15,30,45,1,25,1,75,150,225,1,125,1,375,750,1125,1,625,
%T A328112 1250,1875,3750,5625,1,31,1,80,42,63,126,60,1,105,210,315,1,175,1,525,
%U A328112 1050,1575,1,875,1750,2625,5250,7875,1,4375,8750,13125,26250,39375,1,92,1,147,294,441,882,245,1,735,1470,2205,1,1225,1,3675,7350,11025,22050
%N A328112 a(1) = 0, for primes p, a(p) = 1, and for any other number n, a(n) = max(A003415(n), A276086(n)).
%C A328112 Apart from primes p, for which a(p) = 1, the only duplicated values among the first 65537 terms are a(30040) = a(32344) = 51108 and a(30150) = a(60278) = 47685.
%H A328112 Antti Karttunen, <a href="/A328112/b328112.txt">Table of n, a(n) for n = 1..2310</a>
%H A328112 Antti Karttunen, <a href="/A328112/a328112.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%e A328112 As 30150 is not a prime, a(30150) = max(A003415(30150), A276086(30150)) = max(47685, 40817) = 47685.
%e A328112 As 60278 is not a prime, a(60278) = max(A003415(60278), A276086(60278)) = max(30141, 47685) = 47685.
%o A328112 (PARI)
%o A328112 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A328112 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 A328112 A328112(n) = if(1==n,0,if(isprime(n),1,max(A003415(n),A276086(n))));
%Y A328112 Cf. A003415, A048103, A129251, A276085, A276086, A327858, A327859, A327928, A327929, A327963, A327965, A328097, A328098, A328099.
%K A328112 nonn
%O A328112 1,4
%A A328112 _Antti Karttunen_, Oct 07 2019