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A366181 The number of 2n-digit integers that can be written as the product of two n-digit integers.

%I A366181 #32 Sep 08 2024 08:25:40
%S A366181 27,2205,194700,17874052,1678273759,159696501022,15330248094326,
%T A366181 1480695423269672
%N A366181 The number of 2n-digit integers that can be written as the product of two n-digit integers.
%e A366181 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
%e A366181 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.
%o A366181 (Python)
%o A366181 def A366181(n):
%o A366181     a, b, c, d = 10**(n-1), 10**n, 10**((n<<1)-1), 10**(n<<1)
%o A366181     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
%Y A366181 Cf. A003991, A027424, A366165.
%K A366181 nonn,base,hard,more
%O A366181 1,1
%A A366181 _Clive Tooth_, Oct 03 2023
%E A366181 a(6) from _Hugo Pfoertner_, Oct 12 2023
%E A366181 a(7) from _Bert Dobbelaere_, Oct 23 2023
%E A366181 a(8) from _Clive Tooth_ and _Benjamin Chaffin_, Nov 06 2023