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A337201 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(A337194(i)) = A278221(A337194(j)), for all i, j >= 1.

%I A337201 #6 Aug 20 2020 21:25:27
%S A337201 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 A337201 1,6,3,1,1,6,5,1,4,5,3,3,1,1,7,8,3,3,2,1,3,1,4,6,1,5,1,1,2,1,5,3,4,1,
%U A337201 1,3,3,2,9,7,1,4,1,5,4,8,10,1,5,1,2,11,1,6,6,12,1,5,1,3,1,1,3,13,3,14,15,2,2,16,1
%N A337201 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(A337194(i)) = A278221(A337194(j)), for all i, j >= 1.
%C A337201 Restricted growth sequence transform of f(n) = A278221(A337194(n)).
%C A337201 For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A337198(i) = A337198(j).
%H A337201 Antti Karttunen, <a href="/A337201/b337201.txt">Table of n, a(n) for n = 1..65537</a>
%H A337201 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A337201 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A337201 (PARI)
%o A337201 up_to = 65537;
%o A337201 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 A337201 A000265(n) = (n>>valuation(n, 2));
%o A337201 A337194(n) = (1+A000265(sigma(n)));
%o A337201 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A337201 A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
%o A337201 A278221(n) = A046523(A122111(n));
%o A337201 v337201 = rgs_transform(vector(up_to, n, A278221(A337194(n))));
%o A337201 A337201(n) = v337201[n];
%Y A337201 Cf. A000203, A000265, A278221, A161942, A336698, A337194, A337198.
%Y A337201 Cf. also A286621, A324400, A337200.
%K A337201 nonn
%O A337201 1,9
%A A337201 _Antti Karttunen_, Aug 20 2020