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wasteful numbers
A number  $n$  is called wasteful if the number of digits in its prime factorization (including exponents greater than 1) is greater than the number of digits of  $n$.

For example,  $52=2^2\cdot13$  is a wasteful number since its factorization uses 4 digits.

Some authors call the wasteful numbers extravagant or prodigal.

The numbers which are not wasteful are called economical.

The first wasteful numbers are 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 more terms

Below, the spiral pattern of wasteful numbers up to  $250^2$. See the page on prime numbers for an explanation and links to similar pictures.

spiral pattern of wasteful numbers

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
remainders of wasteful numbers

A graph displaying how many wasteful numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.
divisibility of wasteful numbers
Useful links Mathworld, Wasteful Number
Wikipedia, Extravagant number
OEIS, Sequence A046760
Wasteful numbers can also be... (you may click on names or numbers and on + to get more values)

ABA 18 24 50 + 9999392 aban 12 18 20 + 9000999 abundant 12 18 20 + 9999996 Achilles 72 108 200 + 9999392 admirable 12 20 24 + 9999942 alternating 12 18 30 + 9898989 amenable 12 20 24 + 9999997 amicable 220 284 1210 + 9892936 anti-perfect 244 285 133857 apocalyptic 218 220 222 + 29999 arithmetic 20 22 30 + 9999999 astonishing 204 216 429 + 7103835 automorphic 76 376 9376 Bell 52 4140 21147 + 4213597 betrothed 48 75 140 + 9345903 binomial 20 28 36 + 9997156 brilliant 143 187 209 + 9999811 c.decagonal 451 551 781 + 9989911 c.heptagonal 22 148 253 + 9990436 c.nonagonal 28 55 91 + 9997156 c.octagonal 225 441 1089 + 9966649 c.pentagonal 51 76 226 + 9995001 c.square 85 221 481 + 9994921 c.triangular 46 85 136 + 9996214 cake 26 42 93 + 9963072 Canada 8549 Carmichael 561 1105 1729 + 9890881 Carol 959 65023 261119 Catalan 42 132 429 + 9694845 compositorial 24 congruent 20 22 24 + 9999999 constructible 12 20 24 + 8947712 cube 216 27000 74088 + 9261000 Cullen 65 385 897 + 9961473 Cunningham 24 26 28 + 9999999 Curzon 18 26 30 + 9999990 cyclic 33 51 65 + 9999997 D-number 33 39 51 + 7043133 d-powerful 24 63 132 + 9999865 de Polignac 905 959 1199 + 9999997 decagonal 52 85 126 + 9993501 deceptive 91 451 481 + 9989161 deficient 22 26 33 + 9999999 dig.balanced 12 38 42 + 9999996 double fact. 48 945 10395 + 2027025 droll 72 240 672 + 9461760 Duffinian 36 39 50 + 9999997 eban 30 34 36 + 6066066 emirpimes 26 39 51 + 9999998 eRAP 20 24 98 + 9960047 esthetic 12 34 45 + 9898989 Eulerian 26 57 66 + 9738114 evil 12 18 20 + 9999999 factorial 24 120 720 + 40320 fibodiv 28 75 244 + 9869390 Fibonacci 34 55 144 + 9227465 Friedman 126 153 216 + 999964 gapful 100 108 110 + 9999990 Gilda 78 110 152 + 4484776 Giuga 30 858 1722 66198 happy 28 44 68 + 9999992 harmonic 28 140 270 + 8872200 Harshad 12 18 20 + 9999990 heptagonal 18 34 55 + 9997000 hex 91 721 817 + 9997351 hexagonal 28 45 66 + 9997156 highly composite 12 24 36 + 8648640 hoax 22 58 84 + 9999922 Hogben 57 91 273 + 9995083 house 78 434 652 + 9867520 hungry 74 144 37929 + 7339199 hyperperfect 28 325 496 + 9699181 iban 12 20 22 + 777777 iccanobiF 39 124 514 + 9679838 idoneal 12 18 22 + 1848 inconsummate 62 63 65 + 999995 insolite 11112 interprime 12 18 26 + 9999982 Jacobsthal 85 171 341 + 5592405 Jordan-Polya 12 24 36 + 9676800 junction 117 202 204 + 9999961 Kaprekar 45 55 99 + 9999999 katadrome 20 30 40 + 9876543 Kynea 4223 4198399 Lehmer 51 85 91 + 9997351 Leyland 54 57 100 + 8389137 lonely 120 1340 1341 + 4652430 Lucas 18 76 322 + 7881196 lucky 33 51 63 + 9999997 Lynch-Bell 12 24 36 + 9867312 magic 34 65 260 + 9951391 magnanimous 12 20 30 + 9959374 metadrome 12 18 24 + 3456789 modest 26 39 46 + 9999999 Moran 18 42 45 + 9999950 Motzkin 51 323 835 + 6536382 narcissistic 153 370 407 + 9926315 nialpdrome 20 22 30 + 9999999 nonagonal 24 46 75 + 9992125 nude 12 22 24 + 9999999 O'Halloran 12 20 36 + 924 oban 12 18 20 + 999 octagonal 40 65 96 + 9999176 odious 22 26 28 + 9999998 palindromic 22 33 44 + 9999999 pancake 22 46 56 + 9997157 panconsummate 12 18 20 + 3097 pandigital 75 78 99 + 9998170 partition 22 30 42 + 9289091 pentagonal 12 22 51 + 9998795 perfect 28 496 8128 pernicious 12 18 20 + 9999998 Perrin 12 22 39 + 9141872 plaindrome 12 18 22 + 9999999 Poulet 341 561 645 + 9995671 power 36 100 144 + 9998244 powerful 36 72 100 + 9999392 practical 12 18 20 + 9999990 prim.abundant 12 18 20 + 9999942 primeval 10136 1012349 1023457 primorial 30 210 2310 + 9699690 pronic 12 20 30 + 9995082 Proth 33 57 65 + 9998337 pseudoperfect 12 18 20 + 999999 rare 65 621770 repdigit 22 33 44 + 9999999 repfigit 28 75 742 + 7913837 repunit 40 57 63 + 9995083 Rhonda 4752 5265 5439 + 9892552 Ruth-Aaron 24 50 77 + 9997417 Saint-Exupery 60 480 780 + 9982500 Sastry 328 528 715 + 2975208 self 20 42 75 + 9999998 self-describing 22 4444 224444 + 666666 semiprime 22 26 33 + 9999998 sliding 20 52 65 + 9868025 Smith 22 58 85 + 9999922 sphenic 30 42 66 + 9999994 square 36 100 144 + 9998244 star 253 793 1441 + 9992341 straight-line 210 222 234 + 9999999 strobogrammatic 69 88 96 + 9998666 subfactorial 44 1854 14833 133496 super Niven 12 20 24 + 9990000 super-d 69 190 231 + 9999981 superabundant 12 24 36 + 8648640 tau 12 18 24 + 9999992 taxicab 1729 4104 13832 + 9560896 tcefrep 498906 tetrahedral 20 56 84 + 9962680 tetranacci 56 108 208 + 7555935 triangular 28 36 45 + 9997156 tribonacci 24 44 274 + 8646064 trimorphic 24 51 75 + 9999999 uban 12 18 20 + 9000099 Ulam 18 26 28 + 9999999 undulating 171 202 212 + 9898989 unprimeable 200 204 206 + 9999988 untouchable 52 88 96 + 999996 upside-down 28 46 55 + 9995111 vampire 1260 1395 1530 + 939658 weird 70 836 4030 + 999670 Wieferich 3279 7651 14209 + 6161805 Woodall 63 80 323 + 9961471 Zeisel 1419 1729 1885 + 9773731 Zuckerman 12 24 36 + 9716112 Zumkeller 12 20 24 + 99996 zygodrome 22 33 44 + 9999999