A375774 The number of n-digit integers that can be written as the product of n single-digit integers. The single-digit integers need not be distinct.

10, 27, 55, 85, 108, 119, 118, 108, 94, 78, 60, 46, 35, 27, 19, 14, 10, 7, 4, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Clive Tooth, Aug 27 2024

Keywords

• nonn
• base

Comments

a(21)=1 (9^21 has 21 digits). For all n>21, a(n)=0.

Examples

			a(2) is 27 because 27 2-digit integers can be written as the product of 2 single-digit integers. Those 27 integers are: 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 54, 56, 63, 64, 72 and 81. Note that each of the 2-digit integers 12, 16, 18, 24 and 36 can be expressed as a product of 2 single-digit integers in more than 1 way. However, each of those 2-digit integers is only counted once.
		

Links

• Index entries for eventually constant sequences

Crossrefs

Cf. A366181.

Programs

Python

from math import prod
from itertools import combinations_with_replacement as cwr
def a(n):
    if n > 21: return 0
    L, U = (n>1)*10**(n-1)-1, 10**n
    return len(set(p for mc in cwr(range(10), n) if L < (p:=prod(mc)) < U))
print([a(n) for n in range(1, 22)]) # Michael S. Branicky, Aug 27 2024