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Rhonda numbers
A number    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 than  .

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  .

Rhonda numbers can also be... (you may click on names or numbers and on + to get more values)