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A061209 Numbers which are the cubes of their digit sum. 16
0, 1, 512, 4913, 5832, 17576, 19683 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
It can be shown that 19683 = (1 + 9 + 6 + 8 + 3)^3 = 27^3 is the largest such number.
Numbers of Dudeney. - Philippe Deléham, May 11 2013
If a number n has d digits, 10^(d-1) <= n < 10^d, the cube of the digit sum is at most (d*9)^3 = 729*d^3; if d > 6 this is strictly smaller than 10^(d-1) and cannot be equal to n. See also A061211. - M. F. Hasler, Apr 12 2015
REFERENCES
H. E. Dudeney, 536 Puzzles & Curious Problems, Souvenir Press, London, 1966, p. 36, #120.
Amarnath Murthy, The largest and the smallest m-th power whose digit sum is the m-th root. (To be published)
LINKS
Henk Koppelaar and Peyman Nasehpour, On Hardy's Apology Numbers, arXiv:2008.08187 [math.NT], 2020.
Wikipedia, Dudeney number
FORMULA
a(n) = A007953(a(n))^3. - M. F. Hasler, Apr 12 2015
EXAMPLE
4913 = (4 + 9 + 1 + 3)^3.
MATHEMATICA
Select[Range[20000], Total[IntegerDigits[#]]^3==#&] (* Harvey P. Dale, Apr 11 2015 *)
PROG
(PARI) for(n=0, 999999, sumdigits(n)^3==n&&print1(n", ")) \\ M. F. Hasler, Apr 12 2015
CROSSREFS
Sequence in context: A186845 A239917 A114287 * A017259 A017367 A254899
KEYWORD
nonn,fini,full,base
AUTHOR
Amarnath Murthy, Apr 21 2001
EXTENSIONS
Initial term 0 added by M. F. Hasler, Apr 12 2015
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)