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A366798 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366797(i) = A366797(j) for all i, j >= 0, where A366797 is the number of odd divisors permuted by A163511.

%I A366798 #7 Oct 27 2023 13:11:42
%S A366798 1,1,1,2,1,3,2,2,1,4,3,3,2,4,2,2,1,5,4,4,3,6,3,3,2,6,4,4,2,4,2,2,1,6,
%T A366798 5,5,4,7,4,4,3,8,6,6,3,6,3,3,2,7,6,6,4,7,4,4,2,6,4,4,2,4,2,2,1,9,6,6,
%U A366798 5,10,5,5,4,11,7,7,4,7,4,4,3,11,8,8,6,11,6,6,3,8,6,6,3,6,3,3,2,10,7,7,6,11,6,6
%N A366798 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366797(i) = A366797(j) for all i, j >= 0, where A366797 is the number of odd divisors permuted by A163511.
%C A366798 Restricted growth sequence transform of A366797.
%H A366798 Antti Karttunen, <a href="/A366798/b366798.txt">Table of n, a(n) for n = 0..65537</a>
%H A366798 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%o A366798 (PARI)
%o A366798 up_to = 65537;
%o A366798 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 A366798 A001227(n) = numdiv(n>>valuation(n, 2));
%o A366798 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 A366798 A366797(n) = A001227(A163511(n));
%o A366798 v366798 = rgs_transform(vector(1+up_to,n,A366797(n-1)));
%o A366798 A366798(n) = v366798[1+n];
%Y A366798 Cf. A113415, A163511, A366797.
%Y A366798 Cf. also A366806, A366874.
%K A366798 nonn
%O A366798 0,4
%A A366798 _Antti Karttunen_, Oct 27 2023