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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).
1
8, 41, 140, 367, 789, 1432, 2276, 3280, 4326, 5350, 6254, 7009, 7588, 7970, 8175, 8210, 8120, 7923, 7633, 7272, 6877, 6445, 6013, 5555, 5122, 4693, 4298, 3901, 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
OFFSET
1,1
COMMENTS
As A066310 is finite there exists m such that a(n) = 0 for all n > m.
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
EXAMPLE
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}.
PROG
(Python)
from math import prod
from itertools import combinations_with_replacement as cwr
def c(digs): return int("".join(map(str, digs))) < prod(digs) * sum(digs)
def a(n): return sum(1 for u in cwr(range(1, 10), n) if c(u))
print([a(n) for n in range(1, 16)]) # Michael S. Branicky, Mar 05 2021
(PARI) See PARI link
CROSSREFS
Sequence in context: A250322 A135797 A171714 * A304160 A133106 A358588
KEYWORD
nonn,easy,base
AUTHOR
David A. Corneth, Mar 05 2021
EXTENSIONS
a(27)-a(41) from Michael S. Branicky, Mar 05 2021
STATUS
approved