A046760 Wasteful numbers.

4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 108, 110, 114

Offset

1,1

Comments

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).

A050252(a(n)) > A055642(a(n)). - Reinhard Zumkeller, Jun 21 2011

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

J.-P. Delahaye, Les chasseurs de nombres premiers.

R. G. E. Pinch, Economical numbers., arXiv:math/9802046 [math.NT], 1998.

Eric Weisstein's World of Mathematics, Wasteful Number.

Wikipedia, Extravagant number.

Example

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]

Mathematica

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

Prog

(Haskell)
a046760 n = a046760_list !! (n-1)
a046760_list = filter (\n -> a050252 n > a055642 n) [1..]
-- Reinhard Zumkeller, Aug 02 2013
(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
(Python)
from itertools import count, islice
from sympy import factorint
def A046760_gen(): # generator of terms
    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()))
A046760_list = list(islice(A046760_gen(), 20)) # Chai Wah Wu, Feb 18 2022

Crossrefs

Cf. A046758, A046759.

Sequence in context: A344030 A350706 A036310 * A115684 A020201 A292079

Adjacent sequences: A046757 A046758 A046759 * A046761 A046762 A046763

Keyword

nonn,nice,base,easy

Author

N. J. A. Sloane

Status

approved