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

Author

Antti Karttunen, Dec 03 2024

Keywords

• nonn

Comments

Inverse Möbius transform of A378647.

Links

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

Crossrefs

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

Programs

PARI

A074206(n) = if(n>1, sumdiv(n, i, if(iA074206(i))), n);
A067824(n) = if(1==n,n,2*A074206(n));
A378648(n) = sumdiv(n,d,A067824(d)*A103977(n/d))

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).