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economical numbers
A number  $n$  is called economical if the number of digits in its prime factorization (including exponents greater than 1) is not greater than the number of digits of  $n$.

In practice, economical numbers are the union of equidigital and frugal numbers.

For example,  $121=11^2$  and  $1024=2^{10}$  are both economical.

Some authors call the frugal numbers economical.

The numbers which are not economical are called wasteful.

The first economical numbers are 2, 3, 5, 7, 10, 11, 13, 14, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 37, 41, 43, 47, 49, 53, 59, 61, 64 more terms

The smallest 3 × 3 magic square whose entries are consecutive economical numbers is

245229243
237239241
235249233

Below, the spiral pattern of economical numbers up to  $200^2$. See the page on prime numbers for an explanation and links to similar pictures.

spiral pattern of economical numbers

Economical numbers can also be... (you may click on names or numbers and on + to get more values)

a-pointer 11 13 101 + 19993951 ABA 32 64 81 + 19983842 aban 10 11 13 + 20000000 abundant 112 160 162 + 20000000 Achilles 1125 1152 1323 + 20000000 admirable 224 1372 1504 + 8382464 alt.fact. 19 101 619 + 3301819 alternating 10 14 16 + 18989878 amenable 13 16 17 + 20000000 amicable 1184 122368 2090656 + 19154336 apocalyptic 157 192 224 + 30000 arithmetic 11 13 14 + 9999991 astonishing 15 27 1863 automorphic 25 625 90625 + 12890625 balanced p. 53 157 173 + 19999981 Bell 15 203 877 115975 bemirp 1061 1091 1601 + 19986091 binomial 10 15 21 + 19961721 brilliant 10 14 15 + 19999979 c.decagonal 11 31 61 + 19990001 c.heptagonal 43 71 106 + 19967263 c.nonagonal 10 1081 1225 + 19911205 c.octagonal 25 49 81 + 19989841 c.pentagonal 16 31 106 + 19930381 c.square 13 25 41 + 19964881 c.triangular 10 19 31 + 19989226 cake 15 64 1351 + 19250624 Canada 125 581 16999 Carmichael 10585 15841 1193221 + 19384289 Carol 47 223 3967 + 16769023 Catalan 14 Chen 11 13 17 + 19999739 compositorial 192 1728 17280 + 2903040 congruent 13 14 15 + 9999991 constructible 10 15 16 + 17895424 cube 27 64 125 + 19902511 Cullen 25 161 2049 1048577 Cunningham 10 15 17 + 19980901 Curzon 14 21 29 + 19999953 cyclic 11 13 15 + 9999991 D-number 15 21 111 + 2999949 d-powerful 43 89 135 + 9997263 de Polignac 127 149 251 + 19999963 decagonal 10 27 175 + 19582837 deceptive 259 4187 10001 + 19965037 deficient 10 11 13 + 9999991 dig.balanced 10 11 15 + 16771072 double fact. 15 105 384 + 10321920 droll 2240 5184 6272 + 19005440 Duffinian 16 21 25 + 9999803 eban 32 64 2000 + 6064000 emirp 13 17 31 + 19999981 emirpimes 15 49 115 + 19999979 enlightened 250 256 2048 + 13436683 equidigital 10 11 13 + 19999999 eRAP 7625 68479 162810 + 19312223 esthetic 10 21 23 + 12343454 Eulerian 11 1013 1191 + 13824739 evil 10 15 17 + 20000000 factorial 362880 3628800 fibodiv 14 19 47 + 19999999 Fibonacci 13 21 89 + 1346269 Friedman 25 121 125 + 996543 frugal 125 128 243 + 20000000 gapful 105 121 135 + 20000000 Gilda 29 49 683 + 4848955 good prime 11 17 29 + 19988359 happy 10 13 19 + 10000000 Harshad 10 21 27 + 20000000 heptagonal 81 112 189 + 19792269 hex 19 37 61 + 19945987 hexagonal 15 1225 1431 + 19955403 hoax 160 166 250 + 19999858 Hogben 13 21 31 + 19994313 Honaker 131 263 457 + 19984511 house 32 155 271 + 16838677 hungry 17 2003 161449 2401519 hyperperfect 21 301 1333 + 18116737 iban 10 11 14 + 777743 iccanobiF 13 1053 4139 idoneal 10 13 15 + 177 impolite 16 32 64 + 16777216 inconsummate 161 173 371 + 999953 insolite 111 1122112 interprime 15 21 64 + 19999858 Jacobsthal 11 21 43 + 2796203 Jordan-Polya 16 32 64 + 19906560 junction 101 103 105 + 19999946 Kaprekar 17344 148149 katadrome 10 21 31 + 9875321 Kynea 23 79 287 + 16785407 Lehmer 15 133 259 + 19981237 Leyland 17 32 145 + 16797952 lonely 23 53 211 + 12623189 Lucas 11 29 47 + 12752043 lucky 13 15 21 + 9999823 Lynch-Bell 15 128 135 + 1687392 m-pointer 23 61 1123 + 19122211 magic 15 111 175 + 18797855 magnanimous 11 14 16 + 8608081 metadrome 13 14 15 + 13456789 modest 13 19 23 + 19999999 Moran 21 27 111 + 19999709 Motzkin 21 127 15511 narcissistic 371 nialpdrome 10 11 21 + 20000000 nonagonal 111 1216 1491 + 19769509 nude 11 15 111 + 19999791 oban 10 11 13 + 997 octagonal 21 133 1281 + 19979521 odious 11 13 14 + 19999999 Ormiston 1913 1931 18379 + 19996297 palindromic 11 101 111 + 18800881 palprime 11 101 131 + 9989899 pancake 11 16 29 + 19999651 panconsummate 10 11 14 + 1291 pandigital 11 15 19 + 16434817 partition 11 15 101 + 10619863 pentagonal 35 145 287 + 19927215 pernicious 10 11 13 + 9999991 Perrin 10 17 29 + 16042867 Pierpont 13 17 19 + 19131877 plaindrome 11 13 14 + 19999999 Poulet 1387 2047 2701 + 19985269 power 16 25 27 + 19998784 powerful 16 25 27 + 20000000 practical 16 32 64 + 10000000 prim.abundant 1184 1312 1376 + 19991936 prime 11 13 17 + 19999999 primeval 13 37 107 + 12345679 pronic 16256 16512 65792 + 19514306 Proth 13 17 25 + 19996673 pseudoperfect 112 160 162 + 1000000 repdigit 11 111 11111 1111111 repfigit 14 19 47 + 1084051 repunit 13 15 21 + 19994313 Rhonda 1568 2835 5832 + 18552839 Ruth-Aaron 15 16 25 + 19968209 Saint-Exupery 3840 12960 30720 + 19710540 Sastry 183 self 31 53 64 + 19999999 self-describing 10123133 10153133 10153331 + 19333115 semiprime 10 14 15 + 19999982 sliding 11 25 29 + 20000000 Smith 27 121 166 + 19999858 sphenic 105 1005 1015 + 19999985 square 16 25 49 + 19998784 star 13 37 73 + 19994701 straight-line 111 123 135 + 1234567 strobogrammatic 11 101 111 + 19996661 strong prime 11 17 29 + 19999999 subfactorial 265 1334961 super Niven 10 1000 2000 + 20000000 super-d 19 31 81 + 9999931 tau 128 384 448 + 19999872 taxicab 110808 134379 149389 + 18673625 tetrahedral 10 35 12341 + 19131795 tetranacci 15 29 401 + 14564533 triangular 10 15 21 + 19961721 tribonacci 13 81 149 + 15902591 trimorphic 25 49 125 + 12890625 truncatable prime 13 17 23 + 19981373 twin 11 13 17 + 19999549 uban 10 11 13 + 20000000 Ulam 11 13 16 + 10000241 undulating 101 121 131 + 5656565 unprimeable 320 512 625 + 10000000 untouchable 146 162 448 + 998144 upside-down 19 37 64 + 19982119 vampire 1435 2187 108135 + 19847025 weak prime 13 19 23 + 19999927 weakly prime 294001 505447 584141 + 19851991 Wieferich 1093 3511 10533 17555 Woodall 17 23 159 + 14680063 Zeisel 105 233569 1073305 + 18175361 Zuckerman 11 15 111 + 19922112 Zumkeller 112 160 192 + 100000 zygodrome 11 111 6655 + 11999933