### Friedman Numbers

This collection was established on 15 July 2009 after a nBAB for the number 128 was posted.

```       25,  121,  125,  126,  127,  128,  153,  216,
289,  343,  347,  625,  688,  736, 1022, 1024,
1206, 1255, 1260, 1285, 1296, 1395, 1435, 1503,
1530, 1792, 1827, 2048, 2187, 2349, 2500, 2501,
2502, 2503, 2504, 2505, 2506, 2507, 2508, 2509,
2592, 2737, 2916, 3125, 3159, 3281, 3375, 3378,
3685, 3784, 3864, 3972, 4088, 4096, 4106, 4167,
4536, 4624, 4628, 5120, 5776, 5832, 6144, 6145,
6455, 6880, 7928, 8092, 8192, 9025, 9216, 9261,
...
```

From OEIS.org: "Friedman numbers: can be written in a nontrivial way using their digits and the operations + - * / ^ and concatenation of digits (but not of results)." {OEIS.org::id:A036057}

Note: A nice Friedman number has a math expression in which the digits are used in the order in which they are found in the number.

##### Update::2009.07.18

MathBabbler spent some time finding math expressions for some of the Friedman numbers.

```     25 = 5^2
121 = 11^2
125 = 5^(2+1)
126 = 21 * 6
127 = 2^7 - 1
128 = 2^(8 - 1)
153 = 51 * 3
216 = 6^3
289 = 17^2
343 = (3 + 4)^3    [nice]
625 = 5^(6 - 2)
688 = 86 * 8
736 = 7 * 3^6      [nice]
1022 = 2^10 - 2
1024 = (4 - 2)^10
....
2048 = 8^4 / 2 + 0
2187 = 27 * 81
2349 = 29 * 3^4
2500 = 50^2 + 0
2501 = 50^2 + 1
2502 = 50^2 + 2
....
```

Note: Writing a computer program to determine if a number is a Friedman number is non-trivial (i.e. MathBabbler thinks it is hard).

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 15 July 2009
``` + added 32 on 13 June 2009 + added 128 on 15 July 2009 + added 2500 on 25 July 2009 + added 4096 on 30 December 2009 + added 1024 on 30 December 2009 + added 8192 on 03 March 2010 + added 343 on 19 March 2010 + added 3125 on 05 September 2011 + added 347 on 13 December 2013 + added 1296 on 26 February 2015 + added 289 on 16 October 2015 ```