A046760 - OEIS

%I #49 Feb 18 2022 19:26:31

%S 4,6,8,9,12,18,20,22,24,26,28,30,33,34,36,38,39,40,42,44,45,46,48,50,

%T 51,52,54,55,56,57,58,60,62,63,65,66,68,69,70,72,74,75,76,77,78,80,82,

%U 84,85,86,87,88,90,91,92,93,94,95,96,98,99,100,102,104,108,110,114

%N Wasteful numbers.

%C Write n as product of primes raised to powers, let D(n) = number of digits in product, l(n) = number of digits in n; sequence gives n such that D(n)>l(n).

%C A050252(a(n)) > A055642(a(n)). - _Reinhard Zumkeller_, Jun 21 2011

%H Reinhard Zumkeller, <a href="/A046760/b046760.txt">Table of n, a(n) for n = 1..10000</a>

%H J.-P. Delahaye, <a href="http://www.lifl.fr/~jdelahay/dnalor/ChasseursNbPr.pdf">Les chasseurs de nombres premiers</a>.

%H R. G. E. Pinch, <a href="https://arxiv.org/abs/math/9802046">Economical numbers.</a>, arXiv:math/9802046 [math.NT], 1998.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WastefulNumber.html">Wasteful Number</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Extravagant_number">Extravagant number</a>.

%e For n = 125 = 5^3, l(n) = 3 but D(n) = 2. So 125 is not a term of this sequence. [clarified by _Derek Orr_, Jan 30 2015]

%t Cases[Range[115], n_ /; Length[Flatten[IntegerDigits[FactorInteger[n] /. 1 -> Sequence[]]]] > Length[IntegerDigits[n]]] (* _Jean-François Alcover_, Mar 21 2011 *)

%o (Haskell)

%o a046760 n = a046760_list !! (n-1)

%o a046760_list = filter (\n -> a050252 n > a055642 n) [1..]

%o -- _Reinhard Zumkeller_, Aug 02 2013

%o (PARI) for(n=1,100,s="";F=factor(n);for(i=1,#F[,1],s=concat(s,Str(F[i,1]));s=concat(s,Str(F[i,2])));c=0;for(j=1,#F[,2],if(F[j,2]==1,c++));if(#digits(n)<#s-c,print1(n,", "))) \\ _Derek Orr_, Jan 30 2015

%o (Python)

%o from itertools import count, islice

%o from sympy import factorint

%o def A046760_gen(): # generator of terms

%o     return (n for n in count(1) if len(str(n)) < sum(len(str(p))+(len(str(e)) if e > 1 else 0) for p, e in factorint(n).items()))

%o A046760_list = list(islice(A046760_gen(),20)) # _Chai Wah Wu_, Feb 18 2022

%Y Cf. A046758, A046759.

%K nonn,nice,base,easy

%O 1,1

%A _N. J. A. Sloane_