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A366392 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366390(i) = A366390(j) for all i, j >= 1, where A366390 is the Dirichlet inverse of A366389.

%I A366392 #12 Oct 23 2023 08:34:23
%S A366392 1,2,3,4,5,6,7,4,4,8,9,4,10,11,12,4,13,4,14,4,15,16,17,4,6,18,4,4,19,
%T A366392 20,21,4,22,23,24,4,25,26,27,4,28,29,30,31,4,32,33,4,34,35,36,37,38,4,
%U A366392 39,4,40,41,42,4,43,44,4,4,45,46,47,4,48,49,50,4,51,52,53,4,54,55,56,4,57,58,59,4,60,61,15,62
%N A366392 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366390(i) = A366390(j) for all i, j >= 1, where A366390 is the Dirichlet inverse of A366389.
%C A366392 Restricted growth sequence transform of A366390.
%C A366392 For all i, j: a(i) = a(j) => A365428(i) = A365428(j) => A359377(i) = A359377(j).
%H A366392 Antti Karttunen, <a href="/A366392/b366392.txt">Table of n, a(n) for n = 1..65537</a>
%o A366392 (PARI)
%o A366392 \\ Needs also program given in A366389:
%o A366392 up_to = 65537;
%o A366392 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 A366392 DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
%o A366392 v366392 = rgs_transform(DirInverseCorrect(vector(up_to,n,A366389(n))));
%o A366392 A366392(n) = v366392[n];
%Y A366392 Cf. A010872, A030101, A057889, A073675, A359377, A365428, A366389, A366390.
%Y A366392 Cf. also A366293.
%K A366392 nonn
%O A366392 1,2
%A A366392 _Antti Karttunen_, Oct 22 2023