A366382 - OEIS

%I #8 Oct 12 2023 16:59:46

%S 1,2,3,4,5,6,7,4,2,8,9,4,10,11,11,4,12,1,13,4,14,15,16,4,7,17,3,4,18,

%T 7,19,4,17,20,15,4,21,22,23,4,24,25,26,4,8,27,28,4,12,11,22,4,29,6,23,

%U 4,30,31,32,4,33,34,11,4,20,10,35,4,36,9,37,4,38,39,23,4,20,40,41,4,7,42,43,4,30,44,34,4,45,5,22

%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A349134(i) = A349134(j) for all i, j >= 1, where A349134 is Dirichlet inverse of Kimberling's paraphrases.

%H Antti Karttunen, <a href="/A366382/b366382.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o up_to = 65537;

%o 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 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 A003602(n) = (1+(n>>valuation(n,2)))/2;

%o v366382 = rgs_transform(DirInverseCorrect(vector(up_to,n,A003602(n))));

%o A366382(n) = v366382[n];

%Y Cf. A003602, A349134.

%K nonn

%O 1,2

%A _Antti Karttunen_, Oct 12 2023