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A335425 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000188(i) = A000188(j) and A335424(i) = A335424(j) for all i, j >= 1.

%I A335425 #6 Jun 13 2020 22:10:10
%S A335425 1,2,2,3,2,4,2,5,6,7,2,5,2,7,4,8,2,9,2,5,7,7,2,10,11,7,9,5,2,12,2,13,
%T A335425 7,7,4,14,2,7,7,15,2,16,2,5,9,7,2,13,17,18,7,5,2,19,7,15,7,7,2,10,2,7,
%U A335425 9,20,7,16,2,5,7,16,2,21,2,7,18,5,4,16,2,13,22,7,2,15,7,7,7,15,2,23,7,5,7,7,7,24,2,25,9,26,2,16,2,15,12
%N A335425 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000188(i) = A000188(j) and A335424(i) = A335424(j) for all i, j >= 1.
%C A335425 Restricted growth sequence transform of the ordered pair [A000188(n), A046523(A335423(n))].
%C A335425 For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A001222(i) = A001222(j).
%H A335425 Antti Karttunen, <a href="/A335425/b335425.txt">Table of n, a(n) for n = 1..65537</a>
%o A335425 (PARI)
%o A335425 up_to = 65537;
%o A335425 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 A335425 A000188(n) = core(n, 1)[2]; \\ From A000188
%o A335425 A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
%o A335425 A248663(n) = A048675(core(n));
%o A335425 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A335425 A335423(n) = A005940(1+A248663(n));
%o A335425 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A335425 Aux335425(n) = [A000188(n),A046523(A335423(n))];
%o A335425 v335425 = rgs_transform(vector(up_to,n,Aux335425(n)));
%o A335425 A335425(n) = v335425[n];
%Y A335425 Cf. A000188, A001222, A046523, A162642, A248663, A305800, A335423, A335424.
%K A335425 nonn
%O A335425 1,2
%A A335425 _Antti Karttunen_, Jun 13 2020