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

1,1

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

Formula

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

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

Prog

(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(d<n, A348717(n/d)*A354186(d), 0)); mapput(memoA354186, n, v); (v)));
A354187(n) = (A348717(n)+A354186(n));

Crossrefs

Cf. A348717, A354186.

Sequence in context: A353369 A323900 A349347 * A349345 A349357 A071390

Adjacent sequences: A354184 A354185 A354186 * A354188 A354189 A354190

Keyword

sign

Author

Antti Karttunen, May 19 2022

Status

approved