is a base-b
Rhonda number if the product of its digits, when represented in base
, is equal to
times the sum of its prime factors.
For example, is a base-10 Rhonda number because
Rhonda numbers exist only in composite bases.
Indeed, the product of the digits of a number in a prime base
cannot be divisible by , since every digit is smaller
Kevin Brown (see link below) has proved that there are
infinite Rhonda numbers.
The first base-10 Rhonda numbers are
1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284 more terms
1000 is the smallest Rhonda number in two bases, namely 16 and 36, since
, and we have
for base 16 and
for base 36.
The first smallest Rhonda numbers with respect to 1, 2,...,10 bases are
560, 1000, 10200, 5670, 63945, 158400, 322920, 140800, 1200420, 889200.
You can download a text file containing the
64507 base-10 Rhonda numbers up to .
Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
A graph displaying how many Rhonda numbers are multiples of the primes p
from 2 to 71. In black the ideal line 1/p