A366296 Lexicographically earliest infinite sequence such that a(i) = a(j) => A346242(i) = A346242(j) for all i, j >= 1, where A346242 is Dirichlet inverse of gcd(n, A276086(n)).

1, 2, 3, 4, 2, 5, 2, 4, 6, 3, 2, 7, 2, 1, 8, 4, 2, 9, 2, 10, 11, 1, 2, 4, 12, 1, 13, 4, 2, 14, 2, 4, 11, 1, 15, 16, 2, 1, 11, 4, 2, 17, 2, 4, 18, 1, 2, 4, 19, 20, 11, 4, 2, 21, 3, 19, 11, 1, 2, 22, 2, 1, 12, 4, 1, 15, 2, 4, 11, 23, 2, 24, 2, 1, 25, 4, 15, 15, 2, 4, 26, 1, 2, 27, 3, 1, 11, 4, 2, 28, 15, 4, 11, 1, 1, 4

Offset

1,2

Comments

Restricted growth sequence transform of A346242.

For all i, j: A305900(i) = A305900(j) => a(i) = a(j) => A008966(i) = A008966(j).

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.
A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
v366296 = rgs_transform(DirInverseCorrect(vector(up_to, n, A324198(n))));
A366296(n) = v366296[n];

Crossrefs

Cf. A008966, A276086, A305900, A324198, A346242.

Cf. also A366297.

Sequence in context: A117826 A322604 A173229 * A191248 A323156 A075994

Adjacent sequences: A366293 A366294 A366295 * A366297 A366298 A366299

Keyword

nonn

Author

Antti Karttunen, Oct 07 2023

Status

approved