A378646 Dirichlet convolution of A000027 and A378643.

1, 1, 1, 2, 1, 3, 1, 4, 2, 3, 1, 4, 1, 3, 3, 8, 1, 4, 1, 6, 3, 3, 1, 8, 2, 3, 4, 8, 1, 1, 1, 16, 3, 3, 3, 10, 1, 3, 3, 10, 1, 1, 1, 8, 8, 3, 1, 16, 2, 8, 3, 8, 1, 12, 3, 12, 3, 3, 1, 10, 1, 3, 8, 32, 3, 1, 1, 8, 3, 9, 1, 16, 1, 3, 8, 8, 3, 1, 1, 20, 8, 3, 1, 8, 3, 3, 3, 16, 1, 14, 3, 8, 3, 3, 3, 32, 1, 8, 8, 14, 1, 1, 1, 18, 13

Offset: 1

Author

Antti Karttunen, Dec 03 2024

Keywords

• sign

Comments

First negative value is a(140) = -2.

Odd bisection is not A352063: a(472*2 + 1) = 102 != A352063(472) = A074206(945) = 132. Note that 945 is the first odd abundant number, A005231.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000027, A005101, A005231, A074206, A103977, A378643, A378645 (Dirichlet inverse).

Programs

PARI

A378646(n) = sumdiv(n,d,d*A378643(n/d));

Formula

a(n) = Sum_{d|n} d*A378643(n/d).

a(n) = A074206(n) if n is a non-abundant number (A263837), and apparently never when n is abundant, A005101.