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A336920 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A329697(n), A331410(n), A336158(n)], for all i, j >= 1.

%I A336920 #6 Aug 10 2020 22:19:05
%S A336920 1,1,2,1,3,2,4,1,5,3,6,2,6,4,7,1,8,5,9,3,10,6,11,2,12,6,13,4,14,7,15,
%T A336920 1,16,8,16,5,14,9,16,3,17,10,18,6,19,11,20,2,21,12,22,6,14,13,23,4,24,
%U A336920 14,25,7,11,15,26,1,23,16,25,8,27,16,18,5,28,14,29,9,27,16,18,3,30,17,9,10,31,18,32,6,28,19,27,11,33,20,32,2,17,21,34,12,28,22,9,6,35
%N A336920 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A329697(n), A331410(n), A336158(n)], for all i, j >= 1.
%C A336920 Restricted growth sequence transform of the triplet [A329697(n), A331410(n), A336158(n)].
%C A336920 For all i, j:
%C A336920   A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j),
%C A336920   a(i) = a(j) => A335880(i) = A335880(j),
%C A336920   a(i) = a(j) => A336391(i) = A336391(j),
%C A336920   a(i) = a(j) => A336471(i) = A336471(j).
%H A336920 Antti Karttunen, <a href="/A336920/b336920.txt">Table of n, a(n) for n = 1..65537</a>
%o A336920 (PARI)
%o A336920 up_to = 65537;
%o A336920 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 A336920 A000265(n) = (n>>valuation(n,2));
%o A336920 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336920 A336158(n) = A046523(A000265(n));
%o A336920 A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
%o A336920 A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
%o A336920 Aux336920(n) = [A329697(n), A331410(n), A336158(n)];
%o A336920 v336920 = rgs_transform(vector(up_to, n, Aux336920(n)));
%o A336920 A336920(n) = v336920[n];
%Y A336920 Cf. A000265, A003602, A324400, A329697, A331410, A335880, A336391, A336471.
%K A336920 nonn
%O A336920 1,3
%A A336920 _Antti Karttunen_, Aug 10 2020