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A366891 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j), A206787(A163511(i)) = A206787(A163511(j)) and A336651(A163511(n)) = A336651(A163511(j)) for all i, j >= 0.

%I A366891 #7 Nov 04 2023 18:24:15
%S A366891 1,1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,14,4,15,8,
%T A366891 16,1,17,9,18,5,19,10,20,3,21,11,22,6,23,12,24,2,25,13,26,7,27,14,28,
%U A366891 4,29,15,30,8,14,16,31,1,32,17,33,9,34,18,35,5,36,19,37,10,38,20,39,3,40,21,41,11,42,22,43,6,44,23
%N A366891 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j), A206787(A163511(i)) = A206787(A163511(j)) and A336651(A163511(n)) = A336651(A163511(j)) for all i, j >= 0.
%C A366891 Restricted growth sequence transform of the triplet [A365425(n), A206787(A163511(n)), A336651(A163511(n))], and also by conjecture, of sequence b(n) = A351040(A163511(n)).
%C A366891 For all i, j >= 0:
%C A366891   a(i) = a(j) => A365395(i) = A365395(j),
%C A366891   a(i) = a(j) => A366874(i) = A366874(j),
%C A366891   a(i) = a(j) => A366881(i) = A366881(j).
%H A366891 Antti Karttunen, <a href="/A366891/b366891.txt">Table of n, a(n) for n = 0..65537</a>
%F A366891 For all n >= 1, a(n) = a(2*n) = a(A000265(n)).
%o A366891 (PARI)
%o A366891 up_to = 65537;
%o A366891 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 A366891 A000265(n) = (n>>valuation(n,2));
%o A366891 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A366891 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 A366891 A365425(n) = A046523(A000265(A163511(n)));
%o A366891 A206787(n) = sumdiv(n, d, d*issquarefree(2*d));
%o A366891 A336651(n) = { my(f=factor(n>>valuation(n,2))); prod(i=1, #f~, f[i,1]^(f[i,2]-1)); };
%o A366891 A366891aux(n) = [A365425(n), A206787(A163511(n)), A336651(A163511(n))];
%o A366891 v366891 = rgs_transform(vector(1+up_to,n,A366891aux(n-1)));
%o A366891 A366891(n) = v366891[1+n];
%Y A366891 Cf. A000265, A000593, A163511, A347385, A351040, A351461, A365425.
%Y A366891 Differs from A366806 for the first time at n=105, where a(105) = 52, while A366806(105) = 19.
%Y A366891 Differs from A366881 for the first time at n=511, where a(511) = 249, while A366881(511) = 7.
%K A366891 nonn
%O A366891 0,4
%A A366891 _Antti Karttunen_, Nov 04 2023