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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. 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 STATUS approved

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Last modified December 7 19:19 EST 2022. Contains 358669 sequences. (Running on oeis4.)