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.

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, 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, 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

Offset

1,2

Comments

Restricted growth sequence transform of A366390.

For all i, j: a(i) = a(j) => A365428(i) = A365428(j) => A359377(i) = A359377(j).

Links

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

Prog

(PARI)
\\ Needs also program given in A366389:
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.
v366392 = rgs_transform(DirInverseCorrect(vector(up_to, n, A366389(n))));
A366392(n) = v366392[n];

Crossrefs

Cf. A010872, A030101, A057889, A073675, A359377, A365428, A366389, A366390.

Cf. also A366293.

Sequence in context: A366382 A138221 A038388 * A272573 A328477 A332230

Adjacent sequences: A366389 A366390 A366391 * A366393 A366394 A366395

Keyword

nonn

Author

Antti Karttunen, Oct 22 2023

Status

approved