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A366181
The number of 2n-digit integers that can be written as the product of two n-digit integers.
2
27, 2205, 194700, 17874052, 1678273759, 159696501022, 15330248094326, 1480695423269672
OFFSET
1,1
EXAMPLE
a(1)=27. That is, when the integers are expressed in decimal, the number of 2-digit integers that can be written as the product of 2 single-digit integers is 27: 10=2*5, 12=2*6=3*4, 14=2*7, 15=3*5, 16=2*8=4*4, 18=2*9=3*6, 20=4*5, 21=3*7, 24=3*8=4*6, 25=5*5, 27=3*9, 28=4*7, 30=5*6, 32=4*8, 35=5*7, 36=4*9=6*6, 40=5*8, 42=6*7, 45=5*9, 48=6*8, 49=7*7, 54=6*9, 56=7*8, 63=7*9, 64=8*8, 72=8*9, 81=9*9
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 2 ways. However, each of those 2-digit integers is only counted once.
PROG
(Python)
def A366181(n):
a, b, c, d = 10**(n-1), 10**n, 10**((n<<1)-1), 10**(n<<1)
return len({i*j for i in range(a, b) for j in range(min(i, c//i), min(b, d//i+1)) if c<=i*j<d}) # Chai Wah Wu, Oct 13 2023
CROSSREFS
KEYWORD
nonn,base,hard,more
AUTHOR
Clive Tooth, Oct 03 2023
EXTENSIONS
a(6) from Hugo Pfoertner, Oct 12 2023
a(7) from Bert Dobbelaere, Oct 23 2023
a(8) from Clive Tooth and Benjamin Chaffin, Nov 06 2023
STATUS
approved