Extravagant number
In number theory, an extravagant number (also known as a wasteful number) is a natural number in a given number base that has fewer digits than the number of digits in its prime factorization in the given number base (including exponents). For example, in base 10, 4 = 22, 6 = 2×3, 8 = 23, and 9 = 32 are extravagant numbers . There are infinitely many extravagant numbers in every base. Mathematical definition
Let  be a number base, and let  be the number of digits in a natural number  for base . A natural number  has the prime factorisation
 
where  is the p-adic valuation of , and  is an extravagant number in base  if

See also 
Equidigital number
Frugal number

Notes

References 
 R.G.E. Pinch (1998), Economical Numbers. Chris Caldwell, The Prime Glossary: extravagant number at The Prime Pages. Base-dependent integer sequences