A366382 - OEIS

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A366382

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.

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, 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, 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

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OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

PROG

(PARI)

up_to = 65537;

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; };

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

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

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

A366382(n) = v366382[n];

CROSSREFS

Cf. A003602, A349134.

Sequence in context: A329606 A115871 A366383 * A138221 A038388 A366392

Adjacent sequences: A366379 A366380 A366381 * A366383 A366384 A366385

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 12 2023

STATUS

approved