A359779 Dirichlet inverse of A359778, where A359778 is the number of factorizations of n into factors not divisible by p^p for any prime p (terms of A048103).

1, -1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 1, -1, 0, 0, 0, -1, 1, -1, 1, 0, 0, -1, 0, -1, 0, 1, 1, -1, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, -1, 1, 1, 0, -1, 0, -1, 1, 0, 1, -1, 1, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 1, -1, 1, 0, 1, -1, 0, -1, 0, 1, 1, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, -1, 1, 1, 0, -1, 1, -1, 0, 1

Offset

1,420

Comments

The first term with absolute value larger than 1 is a(420) = -2.

Links

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

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A359778(n/d) * a(d).

Prog

(PARI)
A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 1]>f[k, 2])); };
A359778(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1) && (d<=m) &&
A359550(d), s += A359778(n/d, d))); (s));
memoA359779 = Map();
A359779(n) = if(1==n, 1, my(v); if(mapisdefined(memoA359779, n, &v), v, v = -sumdiv(n, d, if(d<n, A359778(n/d)*A359779(d), 0)); mapput(memoA359779, n, v); (v)));

Crossrefs

Cf. A048103, A359550, A359778 (Dirichlet inverse).

Sequence in context: A214330 A335909 A266591 * A132194 A354034 A174897

Adjacent sequences: A359776 A359777 A359778 * A359780 A359781 A359782

Keyword

sign

Author

Antti Karttunen, Jan 16 2023

Status

approved