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%I #20 Feb 06 2015 05:51:30
%S 27,108,125,128,129,135,138,143,159,160,184,187,189,196,207,209,216,
%T 219,243,249,256,259,265,276,295,297,329,341,351,375,403,429,451,458,
%U 469,497,512,529,621,625,671,679,729,781,795,837,841,892,896,908,916,932
%N Hyper economical numbers.
%C The distinction between the economical numbers (A046759) is that the distinct digits are counted only instead all digits. Hence the definition:
%C Write n as product of primes raised to powers, let D(n) = total number of distinct digits in product representation (number of distinct digits in all the primes and number of distinct digits in all the exponents that are greater than 1) and nbd(n) = A043537(n) number of distinct digits in n; sequence gives n such that D(n) < nbd(n).
%e 27 is in the sequence because 27 = 3 ^ 3 => D(27)= 1 < nbd(27)=2.
%t Cases[Range[400], n_ /; Length[Union[Flatten[IntegerDigits[FactorInteger[n] /. 1 -> Sequence[]]]]]< Length[Union[Flatten[IntegerDigits[n]]]]]
%o (PARI) for(n=1,10^3,s=[];F=factor(n);for(i=1,#F[,1],s=concat(s,digits(F[i,1]));if(F[i,2]>1,s=concat(s,digits(F[i,2]))));if(#vecsort(digits(n),,8)>#vecsort(s,,8),print1(n,", "))) \\ _Derek Orr_, Jan 30 2015
%Y Cf. A043537, A046760, A046758, A046759, A254318, A254321.
%K nonn,base
%O 1,1
%A _Michel Lagneau_, Jan 28 2015
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