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A337200 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A337194(i)) = A278222(A337194(j)), for all i, j >= 1.

%I A337200 #7 Aug 20 2020 21:25:19
%S A337200 1,1,1,1,1,1,1,1,2,3,1,1,1,1,1,1,3,3,4,5,1,3,1,1,1,5,4,1,1,3,1,1,1,2,
%T A337200 1,6,3,1,1,6,5,1,4,5,3,3,1,1,6,7,3,5,2,1,3,1,4,6,1,5,1,1,2,1,5,3,3,1,
%U A337200 1,3,3,5,5,6,1,3,1,5,4,7,7,1,5,1,2,3,1,6,6,8,1,5,1,3,1,1,5,9,3,10,5,2,2,9,1
%N A337200 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A337194(i)) = A278222(A337194(j)), for all i, j >= 1.
%C A337200 Restricted growth sequence transform of f(n) = A278222(A337194(n)).
%C A337200 For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A337199(i) = A337199(j).
%H A337200 Antti Karttunen, <a href="/A337200/b337200.txt">Table of n, a(n) for n = 1..65537</a>
%H A337200 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A337200 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A337200 (PARI)
%o A337200 up_to = 65537;
%o A337200 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 A337200 A000265(n) = (n>>valuation(n, 2));
%o A337200 A337194(n) = (1+A000265(sigma(n)));
%o A337200 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A337200 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A337200 A278222(n) = A046523(A005940(1+n));
%o A337200 v337200 = rgs_transform(vector(up_to, n, A278222(A337194(n))));
%o A337200 A337200(n) = v337200[n];
%Y A337200 Cf. A000203, A000265, A278222, A161942, A336698, A337194, A337199.
%Y A337200 Cf. also A286622, A324400, A337201.
%K A337200 nonn
%O A337200 1,9
%A A337200 _Antti Karttunen_, Aug 20 2020