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A328765 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A328763(n), except for odd numbers > 1, f(n) = 0.

%I A328765 #5 Oct 28 2019 20:00:38
%S A328765 1,2,3,4,5,4,3,4,5,4,6,4,7,4,6,4,8,4,9,4,10,4,10,4,11,4,10,4,12,4,7,4,
%T A328765 5,4,9,4,9,4,6,4,10,4,13,4,10,4,10,4,14,4,12,4,12,4,15,4,12,4,16,4,13,
%U A328765 4,6,4,8,4,14,4,10,4,10,4,17,4,12,4,12,4,18,4,12,4,19,4,20,4,21,4,19,4,17,4,10,4,12,4,14,4,12,4,12,4,22,4,12,4
%N A328765 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A328763(n), except for odd numbers > 1, f(n) = 0.
%C A328765 For all i, j:
%C A328765   A319701(i) = A319701(j) => a(i) = a(j),
%C A328765   a(i) = a(j) => A328578(i) = A328578(j).
%H A328765 Antti Karttunen, <a href="/A328765/b328765.txt">Table of n, a(n) for n = 0..32768</a>
%H A328765 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A328765 (PARI)
%o A328765 up_to = 32768;
%o A328765 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A328765 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328765 A328613(n) = { my(m=1, p=2); while(n, m *= p^valuation(n,p); n = n\p; p = nextprime(1+p)); (m*p); };
%o A328765 A328763(n) = A328613(A276086(n));
%o A328765 Aux328765(n) = if((n>1)&&(n%2),0,A328763(n));
%o A328765 v328765 = rgs_transform(vector(1+up_to, n, Aux328765(n-1)));
%o A328765 A328765(n) = v328765[1+n];
%Y A328765 Cf. A276086, A319701, A328578, A328613, A328763, A328764.
%K A328765 nonn
%O A328765 0,2
%A A328765 _Antti Karttunen_, Oct 28 2019