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A342034 a(n) is the number of numbers k with n digits where k has digits in nondecreasing order and satisfies k < (product of digits of k) * (sum of digits of k).

%I A342034 #30 Mar 07 2021 01:27:04
%S A342034 8,41,140,367,789,1432,2276,3280,4326,5350,6254,7009,7588,7970,8175,
%T A342034 8210,8120,7923,7633,7272,6877,6445,6013,5555,5122,4693,4298,3901,
%U A342034 3534,3189,2872,2562,2285,2029,1789,1576,1376,1194,1037,893,759,654,548,454,384,315,254,210,168,127,97,79,56,39,31,21,12,8,4
%N A342034 a(n) is the number of numbers k with n digits where k has digits in nondecreasing order and satisfies k < (product of digits of k) * (sum of digits of k).
%C A342034 As A066310 is finite there exists m such that a(n) = 0 for all n > m.
%C A342034 a(n) = 0 for n >= 85 since 9^n*9n <= 10^(n-1) for n >= 85. This may occur as early as n = 60, as 9^n*9n <= 10^n-1 for n >= 60. But a(59) > 0 since 10^59-1 < 9^59*9*59. - _Michael S. Branicky_, Mar 05 2021
%H A342034 David A. Corneth, <a href="/A342034/a342034_1.gp.txt">PARI program</a>
%e A342034 a(1) = 8 as there are 8 one-digit numbers k as described in name. Those are {2, 3, 4, 5, 6, 7, 8, 9}.
%o A342034 (Python)
%o A342034 from math import prod
%o A342034 from itertools import combinations_with_replacement as cwr
%o A342034 def c(digs): return int("".join(map(str, digs))) < prod(digs) * sum(digs)
%o A342034 def a(n): return sum(1 for u in cwr(range(1, 10), n) if c(u))
%o A342034 print([a(n) for n in range(1, 16)]) # _Michael S. Branicky_, Mar 05 2021
%o A342034 (PARI) See PARI link
%Y A342034 Cf. A009994, A066310.
%K A342034 nonn,easy,base
%O A342034 1,1
%A A342034 _David A. Corneth_, Mar 05 2021
%E A342034 a(27)-a(41) from _Michael S. Branicky_, Mar 05 2021