A positive integer n is said to be a Rhonda number to base b if the product of the base b digits of n is equal to b times the sum of n's prime factors.


These numbers were named by Kevin Brown after an acquaintance of his whose residence number was 25662, a member of the base 10 numbers with this property.


25662 is a Rhonda number to base-10. The prime factorization is 2 × 3 × 7 × 13 × 47; the product of its base-10 digits is equal to the base times the sum of its prime factors:

2 × 5 × 6 × 6 × 2 = 720 = 10 × (2 + 3 + 7 + 13 + 47)

Rhonda numbers only exist in bases that are not a prime.

Rhonda numbers to base 10 always contain at least 1 digit 5 and always contain at least 1 even digit.



Task
 For the non-prime bases b from 2 through 16 , find and display here, on this page, at least the first 10 Rhonda numbers to base b. Display the found numbers at least in base 10.


Stretch
 Extend out to base 36.


See also
 Wolfram Mathworld - Rhonda numbers
 Numbers Aplenty - Rhonda numbers
 OEIS:A100968 - Integers n that are Rhonda numbers to base 4
 OEIS:A100969 - Integers n that are Rhonda numbers to base 6
 OEIS:A100970 - Integers n that are Rhonda numbers to base 8
 OEIS:A100973 - Integers n that are Rhonda numbers to base 9
 OEIS:A099542 - Rhonda numbers to base 10
 OEIS:A100971 - Integers n that are Rhonda numbers to base 12
 OEIS:A100972 - Integers n that are Rhonda numbers to base 14
 OEIS:A100974 - Integers n that are Rhonda numbers to base 15
 OEIS:A100975 - Integers n that are Rhonda numbers to base 16
 OEIS:A255735 - Integers n that are Rhonda numbers to base 18
 OEIS:A255732 - Rhonda numbers in vigesimal number system (base 20)
 OEIS:A255736 - Integers that are Rhonda numbers to base 30
 Related Task: Smith numbers




tobase=: (a.{~;48 97(+ i.)each 10 26) {~ #.inv
isrhonda=: (*/@:(#.inv) = (* +/@q:))"0
 
task=: {{
  for_base.(#~ 0=1&p:) }.1+i.36 do.
    k=.i.0
    block=. 1+i.1e4
    while. 15>#k do.
      k=. k, block#~ base isrhonda block
      block=. block+1e4
    end.
    echo ''
    echo 'First 15 Rhondas in',b=.' base ',':',~":base
    echo 'In base 10: ',":15{.k
    echo 'In',;:inv b;base tobase each 15{.k
  end.
}}
 
   task''
 