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

1,4

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

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.

Prog

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

Crossrefs

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

Sequence in context: A249336 A067004 A117920 * A079617 A079616 A292587

Adjacent sequences: A378643 A378644 A378645 * A378647 A378648 A378649

Keyword

sign

Author

Antti Karttunen, Dec 03 2024

Status

approved