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In number theory, a Dudeney number in a given number base is a natural number equal to the perfect cube of another natural number such that the digit sum of the first natural number is equal to the second. The name derives from Henry Dudeney, who noted the existence of these numbers in one of his puzzles, Root Extraction, where a professor in retirement at Colney Hatch postulates this as a general method for root extraction.

For b = 10 (dozenal), there are only 8 such numbers: 0, 1, 5439, 61E4, 705E, 16E68, 18969, 1X8E4

Other powers[]

n Dudeney numbers for nth powers
1 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, X, E,
2 0, 1, X1,
3 0, 1, 5439, 61E4, 705E, 16E68, 18969, 1X8E4,
4 0, 1, 115E41, 492369,
5 0, 1, 11133969, 13271794, 412963E7, 47291768, 5196E139,
6 0, 1, 209281801, 300615369, 371428054, 2109E2EX01, 4366971X61,
7 0, 1, 1975XE416000, 207084590947, 81X7340790E7, 1972389E79605, 429354X8EE6E3, 4E643E468E975,
8 0, 1, 9484246467001, 29742E977026994, 795696EE2979054,
9 0, 1, 6E2X088X07X60000, 4E361056784XX3X83, 54XX47X3574473854,
X 0, 1, 1207X454934340EXE01, 3491E26999645721209,
E 0, 1, 516E42701911600000, 20508E09149887600000, 52X32E08169282810151, 24036E622E976X2238023, 7537E0X268107624X9228, 90X6E5337668X0270E314, 3X8E65965E324E52494714, 42X367750EX359E3E9130E, 552XX3E711598E69860368, 5X97618131924287X9X9E3, 9629393X4651E79X551899,
10 0, 1, 1947311494E1209000000, 15X1262077X9369772772X01, 475XX7194X97E93318342501,
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