A366259 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366258(i) = A366258(j) for all i, j >= 1, where A366258 is Dirichlet inverse of gcd(n, A366275(n)).

1, 2, 3, 4, 5, 6, 5, 4, 4, 7, 5, 4, 5, 7, 8, 4, 5, 4, 5, 4, 9, 7, 5, 4, 10, 7, 11, 4, 5, 12, 5, 4, 9, 7, 3, 4, 5, 7, 9, 4, 5, 13, 5, 4, 13, 7, 5, 4, 4, 14, 8, 4, 5, 15, 16, 4, 8, 7, 5, 4, 5, 7, 17, 4, 1, 13, 5, 4, 9, 6, 5, 4, 5, 7, 18, 4, 19, 13, 5, 4, 20, 7, 5, 4, 3, 7, 9, 4, 5, 21, 19, 4, 9, 7, 1, 4, 5, 4, 17

Offset

1,2

Comments

Restricted growth sequence transform of A366258.

Links

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

Index entries for sequences related to binary expansion of n

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.
A030101(n) = if(n<1, 0, subst(Polrev(binary(n)), x, 2));
A057889(n) = if(!n, n, A030101(n/(2^valuation(n, 2))) * (2^valuation(n, 2)));
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A366275(n) = A163511(A057889(n));
A366283(n) = gcd(n, A366275(n));
v366259 = rgs_transform(DirInverseCorrect(vector(up_to, n, A366283(n))));
A366259(n) = v366259[n];

Crossrefs

Cf. A366275, A366283, A366258.

Sequence in context: A017891 A017881 A017871 * A354153 A017861 A094700

Adjacent sequences: A366256 A366257 A366258 * A366260 A366261 A366262

Keyword

nonn

Author

Antti Karttunen, Oct 07 2023

Status

approved