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A366792 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A366787(i) = A366787(j) for all i, j >= 0.

%I A366792 #9 Jan 03 2024 16:34:00
%S A366792 1,1,1,2,1,3,2,4,1,5,3,6,2,7,4,2,1,8,5,9,3,10,6,3,2,11,7,7,4,12,2,13,
%T A366792 1,14,8,15,5,16,9,5,3,17,10,11,6,18,3,19,2,20,11,10,7,21,7,22,4,18,12,
%U A366792 23,2,22,13,4,1,24,14,25,8,26,15,8,5,27,16,20,9,28,5,29,3,30,17,17,10,31,11,32,6,33,18,34,3
%N A366792 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A366787(i) = A366787(j) for all i, j >= 0.
%C A366792 Restricted growth sequence transform of the ordered pair [A365425(n), A366787(n)].
%C A366792 Restricted growth sequence transform of the function f(n) = A366790(A163511(n)).
%C A366792 For all i, j >= 0: a(i) = a(j) => A366788(i) = A366788(j).
%H A366792 Antti Karttunen, <a href="/A366792/b366792.txt">Table of n, a(n) for n = 0..65537</a>
%F A366792 For all n >= 1, a(n) = a(2*n) = a(A000265(n)).
%o A366792 (PARI)
%o A366792 up_to = 65537;
%o A366792 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 A366792 A000265(n) = (n>>valuation(n,2));
%o A366792 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A366792 A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A366792 A365425(n) = A046523(A000265(A163511(n)));
%o A366792 A366789(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(primepi(f[k, 1]))^f[k, 2]); };
%o A366792 A366787(n) = A366789(A163511(n));
%o A366792 A366792aux(n) = [A365425(n), A366787(n)];
%o A366792 v366792 = rgs_transform(vector(1+up_to,n,A366792aux(n-1)));
%o A366792 A366792(n) = v366792[1+n];
%Y A366792 Cf. A000265, A163511, A365425, A366787.
%Y A366792 Cf. also A365394, A365395.
%K A366792 nonn,look
%O A366792 0,4
%A A366792 _Antti Karttunen_, Oct 23 2023