A366383 Lexicographically earliest infinite sequence such that a(i) = a(j) => A349915(i) = A349915(j) for all i, j >= 1, where A349915 is Dirichlet inverse of arithmetic mean between the number of odd divisors and their sum.

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

Offset

1,2

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
A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));
v366383 = rgs_transform(DirInverseCorrect(vector(up_to, n, A113415(n))));
A366383(n) = v366383[n];

Crossrefs

Cf. A113415, A349915.

Sequence in context: A278059 A329606 A115871 * A366382 A138221 A038388

Adjacent sequences: A366380 A366381 A366382 * A366384 A366385 A366386

Keyword

nonn

Author

Antti Karttunen, Oct 12 2023

Status

approved