A366297 -id:A366297 - cp's OEIS frontend

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

Antti Karttunen, Oct 07 2023

nonn

Restricted growth sequence transform of A346242.

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

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

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

Cf. also A366297.

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(dA324198(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];

A369448 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A327858(i) = A327858(j) and A359589(i) = A359589(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 14, 17, 18, 11, 2, 19, 2, 20, 21, 22, 23, 24, 2, 25, 26, 27, 2, 28, 2, 29, 30, 31, 2, 32, 21, 33, 34, 35, 2, 36, 26, 37, 38, 19, 2, 37, 2, 39, 40, 41, 42, 43, 2, 44, 45, 46, 2, 47, 2, 30, 48, 49, 42, 50, 2, 51, 52, 53, 2, 54, 38, 33, 55

Offset: 1

Antti Karttunen, Jan 26 2024

nonn

Restricted growth sequence transform of the triplet [A003415(n), A327858(n), A359589(n)].

For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A366297(i) = A366297(j).

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

Cf. A003415, A276086, A305800, A327858, A359589, A359595, A366297.

Cf. also A351236, A369047.

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(dA003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A327858(n) = gcd(A003415(n), A276086(n));
v359589 = DirInverseCorrect(vector(up_to,n,A327858(n)-1));
A359589(n) = v359589[n];
Aux369448(n) = [A003415(n), A327858(n), A359589(n)];
v369448 = rgs_transform(vector(up_to, n, Aux369448(n)));
A369448(n) = v369448[n];

cp's OEIS Frontend

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)).

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