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A335880 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329697(i) = A329697(j) and A331410(i) = A331410(j) for all i, j >= 1.

%I A335880 #7 Jul 01 2020 22:27:24
%S A335880 1,1,2,1,3,2,4,1,5,3,5,2,5,4,6,1,7,5,8,3,9,5,9,2,10,5,8,4,11,6,12,1,8,
%T A335880 7,8,5,11,8,8,3,6,9,13,5,11,9,14,2,14,10,10,5,11,8,11,4,15,11,15,6,9,
%U A335880 12,13,1,11,8,15,7,13,8,13,5,16,11,16,8,13,8,13,3,15,6,8,9,17,13,18,5,16,11,13,9,14,14,18,2,6,14,15,10,16,10,8,5,15
%N A335880 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329697(i) = A329697(j) and A331410(i) = A331410(j) for all i, j >= 1.
%C A335880 Restricted growth sequence transform of the ordered pair [A329697(n), A331410(n)].
%C A335880 For all i, j:
%C A335880   A324400(i) = A324400(j) => a(i) = a(j),
%C A335880   a(i) = a(j) => A334861(i) = A334861(j),
%C A335880   a(i) = a(j) => A335875(i) = A335875(j),
%C A335880   a(i) = a(j) => A335877(i) = A335877(j),
%C A335880   a(i) = a(j) => A335881(i) = A335881(j).
%H A335880 Antti Karttunen, <a href="/A335880/b335880.txt">Table of n, a(n) for n = 1..65537</a>
%o A335880 (PARI)
%o A335880 up_to = 65537;
%o A335880 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 A335880 A329697(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A329697(f[k,1]-1)))); };
%o A335880 A331410(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A331410(f[k,1]+1)))); };
%o A335880 Aux335880(n) = [A329697(n),A331410(n)];
%o A335880 v335880 = rgs_transform(vector(up_to, n, Aux335880(n)));
%o A335880 A335880(n) = v335880[n];
%Y A335880 Cf. A329697, A331410, A334861, A335875, A335877, A335881.
%Y A335880 Cf. also A324400, A334867.
%K A335880 nonn
%O A335880 1,3
%A A335880 _Antti Karttunen_, Jun 29 2020