is called aban
if its name (in English)
does not contain the letter "a". The word "and" is not counted
and in general I do not use it when I spell out numbers.
Among the words used to construct numbers names, only the word "thousand"
contains an "a" so the aban numbers are the numbers from 1 to 999,
from 1000000 to 1000999, from 2000000 to 2000999, and so on.
The sum of the reciprocals of aban numbers does not converge and grows slowlytowards infinity.
Aban numbers belong to the same family of eban numbers,
iban numbers, oban numbers, and
uban numbers. All quite boring, if I may speak my mind...
As for the above sets, the definition is not really precise, since
large numbers may have non-standard names.
The first aban numbers are
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 more terms
Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
A graph displaying how many aban numbers are multiples of the primes p
from 2 to 71. In black the ideal line 1/p