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A351080 Lexicographically earliest infinite sequence such that a(i) = a(j) => A324198(i) = A324198(j) and A351083(i) = A351083(j) for all i, j >= 0.

%I A351080 #10 Feb 04 2022 15:59:33
%S A351080 1,2,2,3,4,2,2,5,6,3,7,2,4,2,2,8,9,2,10,2,11,3,2,2,12,13,2,3,4,2,2,2,
%T A351080 4,3,14,15,16,2,2,17,18,2,19,2,12,8,2,2,4,19,13,3,12,2,10,20,21,3,2,2,
%U A351080 4,2,2,22,12,2,2,2,4,3,23,2,24,2,2,25,4,26,2,2,27,3,2,2,28,20,2,3,6,2,10,29,12,3,2,2,4
%N A351080 Lexicographically earliest infinite sequence such that a(i) = a(j) => A324198(i) = A324198(j) and A351083(i) = A351083(j) for all i, j >= 0.
%C A351080 Restricted growth sequence transform of the ordered pair [A324198(n), A351083(n)].
%C A351080 For all i, j: a(i) = a(j) => A351084(i) = A351084(j).
%H A351080 Antti Karttunen, <a href="/A351080/b351080.txt">Table of n, a(n) for n = 0..65537</a>
%o A351080 (PARI)
%o A351080 up_to = 65537;
%o A351080 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 A351080 A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
%o A351080 A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
%o A351080 A351083(n) = gcd(n, A327860(n));
%o A351080 Aux351080(n) = [A324198(n), A351083(n)];
%o A351080 v351080 = rgs_transform(vector(1+up_to,n,Aux351080(n-1)));
%o A351080 A351080(n) = v351080[1+n];
%Y A351080 Cf. A324198, A351083, A351084.
%Y A351080 Cf. also A351085.
%K A351080 nonn,easy,look
%O A351080 0,2
%A A351080 _Antti Karttunen_, Feb 03 2022