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A046760 Wasteful numbers. 10
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 (list; graph; refs; listen; history; text; internal format)
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 [broken link]

R. G. E. Pinch, Economical numbers.

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.

MATHEMATICA

Cases[Range[115], n_ /; Length[Flatten[IntegerDigits[FactorInteger[n] /. 1 -> Sequence[]]]] > Length[IntegerDigits[n]]] (* Jean-Fran├žois 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

CROSSREFS

Cf. A046758, A046759.

Sequence in context: A028958 A200878 A036310 * A115684 A020201 A292079

Adjacent sequences:  A046757 A046758 A046759 * A046761 A046762 A046763

KEYWORD

nonn,nice,base,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Example clarified by Derek Orr, Jan 30 2015

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)