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

Author

Antti Karttunen, Oct 12 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A113415, A349915.

Programs

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(dA113415(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];