Smith number is one in which, the sum of its digits is equal to the sum of the digits in its prime factorization. Smith numbers are composite numbers. Smith numbers were named by Albert Wilansky of Lehigh University, who noticed the property in his brother-in-law Harold Smith's phone number 4937775.
Property: 4937775 = 3 x 5 x 5 x 65837, while 4 + 9 + 3 + 7 + 7 + 7 + 5 = 3 + 5 + 5 + 6 + 5 + 8 + 3 + 7 = 42.
The Smith Numbers Chart shows the list of first few smith numbers from 1 to 10000.
4 | 22 | 27 | 58 |
85 | 94 | 121 | 166 |
202 | 265 | 274 | 319 |
346 | 355 | 378 | 382 |
391 | 438 | 454 | 483 |
517 | 526 | 535 | 562 |
576 | 588 | 627 | 634 |
636 | 645 | 648 | 654 |
663 | 666 | 690 | 706 |
728 | 729 | 762 | 778 |
825 | 852 | 861 | 895 |
913 | 915 | 922 | 958 |
985 | 1086 | 1111 | 1165 |
1219 | 1255 | 1282 | 1284 |
1376 | 1449 | 1507 | 1581 |
1626 | 1633 | 1642 | 1678 |
1736 | 1755 | 1776 | 1795 |
1822 | 1842 | 1858 | 1872 |
1881 | 1894 | 1903 | 1908 |
1921 | 1935 | 1952 | 1962 |
1966 | 2038 | 2067 | 2079 |
2155 | 2173 | 2182 | 2218 |
2227 | 2265 | 2286 | 2326 |
2362 | 2366 | 2373 | 2409 |
2434 | 2461 | 2475 | 2484 |
2515 | 2556 | 2576 | 2578 |
2583 | 2605 | 2614 | 2679 |
2688 | 2722 | 2745 | 2751 |
2785 | 2839 | 2888 | 2902 |
2911 | 2934 | 2944 | 2958 |
3046 | 3091 | 3138 | 3168 |
3174 | 3226 | 3246 | 3258 |
3294 | 3345 | 3366 | 3390 |
3442 | 3505 | 3564 | 3595 |
3615 | 3622 | 3649 | 3663 |
3690 | 3694 | 3802 | 3852 |
3864 | 3865 | 3930 | 3946 |
3973 | 4054 | 4126 | 4162 |
4173 | 4185 | 4189 | 4191 |
4198 | 4209 | 4279 | 4306 |
4369 | 4414 | 4428 | 4464 |
4472 | 4557 | 4592 | 4594 |
4702 | 4743 | 4765 | 4788 |
4794 | 4832 | 4855 | 4880 |
4918 | 4954 | 4959 | 4960 |
4974 | 4981 | 5062 | 5071 |
5088 | 5098 | 5172 | 5242 |
5248 | 5253 | 5269 | 5298 |
5305 | 5386 | 5388 | 5397 |
5422 | 5458 | 5485 | 5526 |
5539 | 5602 | 5638 | 5642 |
5674 | 5772 | 5818 | 5854 |
5874 | 5915 | 5926 | 5935 |
5936 | 5946 | 5998 | 6036 |
6054 | 6084 | 6096 | 6115 |
6171 | 6178 | 6187 | 6188 |
6252 | 6259 | 6295 | 6315 |
6344 | 6385 | 6439 | 6457 |
6502 | 6531 | 6567 | 6583 |
6585 | 6603 | 6684 | 6693 |
6702 | 6718 | 6760 | 6816 |
6835 | 6855 | 6880 | 6934 |
6981 | 7026 | 7051 | 7062 |
7068 | 7078 | 7089 | 7119 |
7136 | 7186 | 7195 | 7227 |
7249 | 7287 | 7339 | 7402 |
7438 | 7447 | 7465 | 7503 |
7627 | 7674 | 7683 | 7695 |
7712 | 7726 | 7762 | 7764 |
7782 | 7784 | 7809 | 7824 |
7834 | 7915 | 7952 | 7978 |
8005 | 8014 | 8023 | 8073 |
8077 | 8095 | 8149 | 8154 |
8158 | 8185 | 8196 | 8253 |
8257 | 8277 | 8307 | 8347 |
8372 | 8412 | 8421 | 8466 |
8518 | 8545 | 8568 | 8628 |
8653 | 8680 | 8736 | 8754 |
8766 | 8790 | 8792 | 8851 |
8864 | 8874 | 8883 | 8901 |
8914 | 9015 | 9031 | 9036 |
9094 | 9166 | 9184 | 9193 |
9229 | 9274 | 9276 | 9285 |
9294 | 9296 | 9301 | 9330 |
9346 | 9355 | 9382 | 9386 |
9387 | 9396 | 9414 | 9427 |
9483 | 9522 | 9535 | 9571 |
9598 | 9633 | 9634 | 9639 |
9648 | 9657 | 9684 | 9708 |
9717 | 9735 | 9742 | 9760 |
9778 | 9840 | 9843 | 9849 |
9861 | 9880 | 9895 | 9924 |
9942 | 9968 | 9975 | 9985 |
The number of Smith numbers below 10n for n=1,2,… is:
1, 6, 49, 376, 3294, 29928, 278411, 2632758, 25154060, 241882509, …
Two consecutive Smith numbers are called Smith brothers.