A378648 Dirichlet convolution of A067824 and A103977, where A067824 is the number of strict chains of divisors starting with n, and A103977 is the Zumkeller deficiency of n.

1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 32, 14, 24, 24, 31, 18, 43, 20, 44, 32, 36, 24, 80, 31, 42, 40, 56, 30, 84, 32, 63, 48, 54, 48, 127, 38, 60, 56, 104, 42, 108, 44, 84, 78, 72, 48, 192, 57, 93, 72, 98, 54, 140, 72, 128, 80, 90, 60, 252, 62, 96, 104, 127, 84, 156, 68, 126, 96, 148, 72, 351, 74, 114, 124, 140, 96

Offset

1,2

Comments

Inverse Möbius transform of A378647.

Links

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

Formula

a(n) = Sum_{d|n} A067824(d)*A103977(n/d).

a(n) = Sum_{d|n} A378647(d).

a(n) = A000203(n) + A378653(n), with a(n) = sigma(n) if and only if n is a non-abundant number (A263837).

Prog

(PARI)
A074206(n) = if(n>1, sumdiv(n, i, if(i<n, A074206(i))), n);
A067824(n) = if(1==n, n, 2*A074206(n));
A378648(n) = sumdiv(n, d, A067824(d)*A103977(n/d))

Crossrefs

Cf. A000203, A005101, A067824, A103977, A263837, A378647 (Möbius transform), A378649, A378653 [= a(n)-sigma(n)].

Sequence in context: A000203 A324545 A003979 * A084250 A090128 A086293

Adjacent sequences: A378645 A378646 A378647 * A378649 A378650 A378651

Keyword

nonn

Author

Antti Karttunen, Dec 03 2024

Status

approved