A366384 Lexicographically earliest infinite sequence such that a(i) = a(j) => A355828(i) = A355828(j) for all i, j >= 1, where A355828 is Dirichlet inverse of A342671, the greatest common divisor of sigma(n) and A003961(n).

1, 2, 3, 4, 3, 5, 3, 6, 7, 5, 3, 8, 3, 5, 1, 9, 3, 7, 3, 10, 1, 5, 3, 11, 7, 5, 12, 8, 3, 2, 3, 13, 1, 5, 1, 7, 3, 5, 1, 14, 3, 2, 3, 15, 7, 5, 3, 7, 7, 7, 1, 8, 3, 11, 1, 16, 2, 5, 3, 17, 3, 5, 7, 18, 19, 2, 3, 20, 1, 2, 3, 11, 3, 5, 7, 8, 1, 2, 3, 21, 4, 5, 3, 4, 1, 5, 2, 22, 3, 7, 1, 15, 1, 5, 1, 23, 3, 7, 24

Offset: 1

Author

Antti Karttunen, Oct 12 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A000203, A003961, A342671, A355828.

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(dA003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A342671(n) = gcd(sigma(n), A003961(n));
v366384 = rgs_transform(DirInverseCorrect(vector(up_to,n,A342671(n))));
A366384(n) = v366384[n];