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

1,1

Comments

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

Links

Table of n, a(n) for n=1..80.

Index entries for eventually constant sequences

Example

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.

Prog

(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

Crossrefs

Cf. A366181.

Sequence in context: A361473 A001107 A103135 * A220021 A008468 A267217

Adjacent sequences: A375771 A375772 A375773 * A375775 A375776 A375777

Keyword

nonn,base

Author

Clive Tooth, Aug 27 2024

Status

approved