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A368695 Lexicographically earliest infinite sequence such that a(i) = a(j) => A368694(i) = A368694(j) for all i, j >= 0.

%I A368695 #11 Jan 04 2024 14:31:19
%S A368695 1,2,3,4,3,5,6,7,3,8,9,10,3,11,12,13,3,14,15,13,3,16,17,18,3,19,13,20,
%T A368695 3,21,11,4,3,22,23,24,3,21,11,25,3,26,27,28,3,29,30,5,3,31,32,33,3,8,
%U A368695 34,21,3,35,36,11,3,20,6,7,3,37,38,39,3,40,41,42,3,35,36,43,3,44,45,8,3,46,47,48,3,49,50,35,3
%N A368695 Lexicographically  earliest infinite sequence such that a(i) = a(j) => A368694(i) = A368694(j) for all i, j >= 0.
%C A368695 Restricted growth sequence transform of A368694, where A368694 is the Dirichlet inverse of the highest power of two that divides sigma(n), applied to A163511(n).
%H A368695 Antti Karttunen, <a href="/A368695/b368695.txt">Table of n, a(n) for n = 0..65537</a>
%o A368695 (PARI)
%o A368695 up_to = 65537;
%o A368695 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 A368695 A082903(n) = (2^valuation(sigma(n), 2));
%o A368695 memoA366889 = Map();
%o A368695 A366889(n) = if(1==n,1,my(v); if(mapisdefined(memoA366889,n,&v), v, v = -sumdiv(n,d,if(d<n,A082903(n/d)*A366889(d),0)); mapput(memoA366889,n,v); (v)));
%o A368695 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 A368695 A368694(n) = A366889(A163511(n));
%o A368695 v368695 = rgs_transform(vector(1+up_to,n,A368694(n-1)));
%o A368695 A368695(n) = v368695[1+n];
%Y A368695 Cf. A163511, A082903, A366889, A368694.
%K A368695 nonn,look
%O A368695 0,2
%A A368695 _Antti Karttunen_, Jan 03 2024