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A351033 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351031(i) = A351031(j), for all i, j >= 1.

%I A351033 #9 Jan 29 2022 22:31:49
%S A351033 1,2,2,2,2,3,2,3,3,4,2,5,2,2,6,7,2,8,2,8,3,9,2,10,4,11,8,12,2,8,2,13,
%T A351033 4,14,4,15,2,12,12,15,2,16,2,4,17,11,2,18,2,19,20,12,2,21,22,13,7,14,
%U A351033 2,23,2,9,24,25,20,26,2,16,12,21,2,27,2,3,28,29,9,30,2,31,32,4,2,33,19,2,20,34,2,35,11,36
%N A351033 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351031(i) = A351031(j), for all i, j >= 1.
%C A351033 Restricted growth sequence transform of A351031.
%H A351033 Antti Karttunen, <a href="/A351033/b351033.txt">Table of n, a(n) for n = 1..65537</a>
%H A351033 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A351033 (PARI)
%o A351033 up_to = 65537;
%o A351033 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 A351033 A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o A351033 A048673(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (1+factorback(f))/2; };
%o A351033 A289813(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
%o A351033 A304759(n) = A289813(A048673(n));
%o A351033 A351031(n) = { my(m=1); fordiv(n,d,if(d<n,m *= A019565(A304759(d)))); (m); };
%o A351033 v351033 = rgs_transform(vector(up_to, n, A351031(n)));
%o A351033 A351033(n) = v351033[n];
%Y A351033 Cf. A019565, A048673, A289813, A304759, A351030, A351031, A351034.
%Y A351033 Cf. also A293223.
%K A351033 nonn,look
%O A351033 1,2
%A A351033 _Antti Karttunen_, Jan 29 2022