A354187 Sum of A348717 and its Dirichlet inverse.

2, 0, 0, 4, 0, 8, 0, 8, 4, 8, 0, 16, 0, 8, 8, 16, 0, 16, 0, 32, 8, 8, 0, 24, 4, 8, 8, 48, 0, 40, 0, 32, 8, 8, 8, 44, 0, 8, 8, 40, 0, 72, 0, 80, 16, 8, 0, 48, 4, 32, 8, 96, 0, 48, 8, 56, 8, 8, 0, 56, 0, 8, 32, 64, 8, 120, 0, 128, 8, 72, 0, 64, 0, 8, 16, 144, 8, 168, 0, 80, 16, 8, 0, 72, 8, 8, 8, 88, 0, 80, 8, 176

Offset: 1

Author

Antti Karttunen, May 19 2022

Keywords

• sign

Comments

The first negative term is a(520) = -8.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A348717, A354186.

Programs

PARI

A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));
memoA354186 = Map();
A354186(n) = if(1==n,1,my(v); if(mapisdefined(memoA354186,n,&v), v, v = -sumdiv(n,d,if(dA348717(n/d)*A354186(d),0)); mapput(memoA354186,n,v); (v)));
A354187(n) = (A348717(n)+A354186(n));

Formula

a(n) = A348717(n) + A354186(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A348717(d) * A354186(n/d).