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

1,2

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

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).

Prog

(PARI) A378647(n) = sumdiv(n, d, moebius(d)*A378648(n/d));
(PARI) A378647(n) = sumdiv(n, d, A074206(d)*A103977(n/d));

Crossrefs

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

Sequence in context: A271839 A290144 A115060 * A004840 A254650 A032994

Adjacent sequences: A378644 A378645 A378646 * A378648 A378649 A378650

Keyword

nonn

Author

Antti Karttunen, Dec 03 2024

Status

approved