A366181 The number of 2n-digit integers that can be written as the product of two n-digit integers.
27, 2205, 194700, 17874052, 1678273759, 159696501022, 15330248094326, 1480695423269672
Offset: 1
Examples
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.
Programs
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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
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