A359778 -id:A359778 - cp's OEIS frontend

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

Antti Karttunen, Jan 16 2023

sign

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

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

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

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(dA359778(n/d)*A359779(d),0)); mapput(memoA359779,n,v); (v)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA359778(n/d) * a(d).

cp's OEIS Frontend

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).

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