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A365392 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 1, where f(n) = [A336158(n), A364255(n), A365425(n)].

%I A365392 #17 Jan 03 2024 16:33:55
%S A365392 1,2,3,4,5,6,7,8,9,10,5,11,12,13,14,15,16,17,18,19,20,10,5,21,22,23,
%T A365392 24,25,12,26,7,27,28,29,30,31,32,33,34,35,36,37,38,19,39,10,5,40,41,
%U A365392 42,43,44,45,46,47,48,20,23,12,49,12,13,50,51,52,53,54,55,56,57,16,58,59,60,61,62,63,64,18,65,66,67,36
%N A365392 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 1, where f(n) = [A336158(n), A364255(n), A365425(n)].
%C A365392 Restricted growth sequence transform of triplet [A336158(n), A364255(n), A365425(n)].
%C A365392 For all i, j >= 1:
%C A365392   a(i) = a(j) => A286531(i) = A286531(j),
%C A365392   a(i) = a(j) => A305891(i) = A305891(j),
%C A365392   a(i) = a(j) => A365391(i) = A365391(j),
%C A365392   a(i) = a(j) => A365421(i) = A365421(j).
%H A365392 Antti Karttunen, <a href="/A365392/b365392.txt">Table of n, a(n) for n = 1..65537</a>
%o A365392 (PARI)
%o A365392 up_to = 65537;
%o A365392 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 A365392 A000265(n) = (n>>valuation(n,2));
%o A365392 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A365392 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 A365392 A364255(n) = gcd(n, A163511(n));
%o A365392 A365392aux(n) = [A364255(n), A046523(A000265(n)), A046523(A000265(A163511(n)))];
%o A365392 v365392 = rgs_transform(vector(up_to,n,A365392aux(n)));
%o A365392 A365392(n) = v365392[n];
%Y A365392 Cf. A000265, A046523, A163511, A286531, A305891, A336158, A364255, A365425, A365391, A365421.
%K A365392 nonn,look
%O A365392 1,2
%A A365392 _Antti Karttunen_, Sep 04 2023