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A351085 Lexicographically earliest infinite sequence such that a(i) = a(j) => A327858(i) = A327858(j) and A345000(i) = A345000(j) for all i, j >= 0.

%I A351085 #10 Feb 04 2022 16:09:19
%S A351085 1,2,3,3,4,3,5,3,6,7,3,3,4,3,8,2,9,3,10,3,11,12,3,3,13,12,14,8,4,3,3,
%T A351085 3,15,16,3,17,18,3,19,2,4,3,3,3,6,8,20,3,21,16,14,12,22,3,10,2,4,2,3,
%U A351085 3,4,3,8,8,23,24,3,3,11,2,3,3,25,3,8,26,27,24,3,3,9,7,3,3,4,2,14,2,28,3,10,2,29,2,30
%N A351085 Lexicographically earliest infinite sequence such that a(i) = a(j) => A327858(i) = A327858(j) and A345000(i) = A345000(j) for all i, j >= 0.
%C A351085 Restricted growth sequence transform of the ordered pair [A327858(n), A345000(n)].
%C A351085 For all i, j >= 1: A305800(i) = A305800(j) => a(i) = a(j).
%C A351085 For all i, j >= 0: a(i) = a(j) => A351086(i) = A351086(j).
%H A351085 Antti Karttunen, <a href="/A351085/b351085.txt">Table of n, a(n) for n = 0..65537</a>
%o A351085 (PARI)
%o A351085 up_to = 65537;
%o A351085 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 A351085 A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
%o A351085 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A351085 A327858(n) = gcd(A003415(n),A276086(n));
%o A351085 A345000(n) = gcd(A003415(n),A003415(A276086(n)));
%o A351085 Aux351085(n) = [A327858(n), A345000(n)];
%o A351085 v351085 = rgs_transform(vector(1+up_to,n,Aux351085(n-1)));
%o A351085 A351085(n) = v351085[1+n];
%Y A351085 Cf. A003415, A276086, A327858, A345000, A351086.
%Y A351085 Cf. also A305800, A351080.
%K A351085 nonn,easy,look
%O A351085 0,2
%A A351085 _Antti Karttunen_, Feb 03 2022