A359788 Dirichlet inverse of A075255, where A075255(n) = n - sopfr(n), where sopfr is the sum of prime factors (with repetition).

1, 0, 0, 0, 0, -1, 0, -2, -3, -3, 0, -5, 0, -5, -7, -8, 0, -10, 0, -11, -11, -9, 0, -15, -15, -11, -18, -17, 0, -20, 0, -22, -19, -15, -23, -25, 0, -17, -23, -29, 0, -30, 0, -29, -34, -21, 0, -33, -35, -38, -31, -35, 0, -37, -39, -43, -35, -27, 0, -42, 0, -29, -50, -48, -47, -50, 0, -47, -43, -56, 0, -38, 0, -35

Offset: 1

Author

Antti Karttunen, Jan 15 2023

Keywords

• sign

Comments

The first positive term after a(1) occurs as a(144) = 13.

Links

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

Crossrefs

Cf. A001414, A075255, A359787 (parity of terms).

Cf. also A359789.

Programs

PARI

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A075255(n) = (n-A001414(n));
memoA359788 = Map();
A359788(n) = if(1==n,1,my(v); if(mapisdefined(memoA359788,n,&v), v, v = -sumdiv(n,d,if(dA075255(n/d)*A359788(d),0)); mapput(memoA359788,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA075255(n/d) * a(d).