A363756 Total number of distinct ways the divisors of n can be the product of other nontrivial divisors of n.

0, 0, 0, 1, 0, 1, 0, 3, 1, 1, 0, 5, 0, 1, 1, 7, 0, 5, 0, 5, 1, 1, 0, 13, 1, 1, 3, 5, 0, 7, 0, 13, 1, 1, 1, 17, 0, 1, 1, 13, 0, 7, 0, 5, 5, 1, 0, 28, 1, 5, 1, 5, 0, 13, 1, 13, 1, 1, 0, 24, 0, 1, 5, 23, 1, 7, 0, 5, 1, 7, 0, 40, 0, 1, 5, 5, 1, 7, 0, 28, 7, 1, 0, 24, 1, 1, 1

Offset

1,8

Comments

Inverse Möbius transform of A001055(n)-1. - Wesley Ivan Hurt, Jul 07 2025

Links

Table of n, a(n) for n=1..87.

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = A057567(n) - A000005(n).

a(n) = Sum_{d|n} (A001055(d)-1).

Example

a(24) = 13 ways: 2*2, 2*3, 2*2*2, 2*4, 2*2*3, 3*4, 2*6, 2*2*2*3, 2*2*6, 2*3*4, 4*6, 2*12, 3*8.

Crossrefs

Cf. A000005 (tau), A001055, A057567.

Sequence in context: A130115 A191582 A356115 * A130160 A288108 A287822

Adjacent sequences: A363753 A363754 A363755 * A363757 A363758 A363759

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jun 20 2023

Status

approved