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A366874 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366873(i) = A366873(j) for all i, j >= 0, where A366873 is the average of number of and sum of odd divisors of n as permuted by A163511.

%I A366874 #7 Oct 27 2023 13:11:51
%S A366874 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 A366874 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 A366874 4,29,15,30,8,14,16,3,1,31,17,32,9,33,18,34,5,35,19,36,10,37,20,38,3,39,21,40,11,41,22,42,6
%N A366874 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366873(i) = A366873(j) for all i, j >= 0, where A366873 is the average of number of and sum of odd divisors of n as permuted by A163511.
%C A366874 Restricted growth sequence transform of A366873.
%H A366874 Antti Karttunen, <a href="/A366874/b366874.txt">Table of n, a(n) for n = 0..65537</a>
%o A366874 (PARI)
%o A366874 up_to = 65537;
%o A366874 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 A366874 A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));
%o A366874 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 A366874 A366873(n) = A113415(A163511(n));
%o A366874 v366874 = rgs_transform(vector(1+up_to,n,A366873(n-1)));
%o A366874 A366874(n) = v366874[1+n];
%Y A366874 Cf. A113415, A163511, A366873.
%Y A366874 Cf. also A366798, A366806, A366878.
%K A366874 nonn
%O A366874 0,4
%A A366874 _Antti Karttunen_, Oct 27 2023