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A366881 Lexicographically earliest infinite sequence such that a(i) = a(j) => A206787(A163511(i)) = A206787(A163511(j)) and A336651(A163511(n)) = A336651(A163511(j)) for all i, j >= 0.

%I A366881 #12 Nov 04 2023 14:00:29
%S A366881 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 A366881 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 A366881 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
%N A366881 Lexicographically earliest infinite sequence such that a(i) = a(j) => A206787(A163511(i)) = A206787(A163511(j)) and A336651(A163511(n)) = A336651(A163511(j)) for all i, j >= 0.
%C A366881 Restricted growth sequence transform of the ordered pair [A206787(A163511(n)), A336651(A163511(n))].
%C A366881 Restricted growth sequence transform of sequence b(n) = A351461(A163511(n)).
%C A366881 For all i, j >= 0:
%C A366881   a(i) = a(j) => A324186(i) = A324186(j), (similarly for A366806)
%C A366881   a(i) = a(j) => A366885(i) = A366885(j). (similarly for A366886).
%H A366881 Antti Karttunen, <a href="/A366881/b366881.txt">Table of n, a(n) for n = 0..65537</a>
%F A366881 For all n >= 1, a(n) = a(2*n) = a(A000265(n)).
%o A366881 (PARI)
%o A366881 up_to = 65537;
%o A366881 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 A366881 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 A366881 A206787(n) = sumdiv(n, d, d*issquarefree(2*d));
%o A366881 A336651(n) = { my(f=factor(n>>valuation(n,2))); prod(i=1, #f~, f[i,1]^(f[i,2]-1)); };
%o A366881 A366881aux(n) = [A206787(A163511(n)), A336651(A163511(n))];
%o A366881 v366881 = rgs_transform(vector(1+up_to,n,A366881aux(n-1)));
%o A366881 A366881(n) = v366881[1+n];
%Y A366881 Cf. A000265, A000593, A163511, A347385, A351461, A366887.
%Y A366881 Cf. also A324186, A366806, A366885, A366886, A366888.
%Y A366881 Differs from A366806 for the first time at n=105, where a(105) = 52, while A366806(105) = 19.
%K A366881 nonn
%O A366881 0,4
%A A366881 _Antti Karttunen_, Nov 04 2023