login
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)).
2
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.
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));
A366283(n) = gcd(n, A366275(n));
v366259 = rgs_transform(DirInverseCorrect(vector(up_to, n, A366283(n))));
A366259(n) = v366259[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 07 2023
STATUS
approved