A378647 Dirichlet convolution of A074206 and A103977, where A074206 is the number of ordered factorizations of n, and A103977 is the Zumkeller deficiency of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 13, 14, 15, 16, 17, 22, 19, 22, 21, 22, 23, 40, 25, 26, 27, 28, 29, 42, 31, 32, 33, 34, 35, 64, 37, 38, 39, 52, 41, 54, 43, 44, 45, 46, 47, 96, 49, 50, 51, 52, 53, 70, 55, 64, 57, 58, 59, 126, 61, 62, 63, 64, 65, 78, 67, 68, 69, 74, 71, 176, 73, 74, 75, 76, 77, 90, 79, 120, 81

Offset: 1

Author

Antti Karttunen, Dec 03 2024

Keywords

• nonn

Comments

Möbius transform of A378648, which is the Dirichlet convolution of A067824 and A103977.

Links

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

Crossrefs

Cf. A000027, A008683, A067824, A074206, A103977, A263837, A378648 (inverse Möbius transform), A378649 (Möbius transform), A378650 [= a(n)-n], A378655 (Dirichlet inverse).

Programs

PARI

A378647(n) = sumdiv(n,d,moebius(d)*A378648(n/d));

PARI

A378647(n) = sumdiv(n,d,A074206(d)*A103977(n/d));

Formula

a(n) = Sum_{d|n} A074206(d)*A103977(n/d).

a(n) = Sum_{d|n} A008683(d)*A378648(n/d).

a(n) = Sum_{d|n} A067824(d)*A378644(n/d).

a(n) = A378650(n)+n, with a(n) = n if and only if n is a non-abundant number (A263837).