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A061209
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Numbers which are the cubes of their digit sum.
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16
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OFFSET
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1,3
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COMMENTS
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It can be shown that 19683 = (1 + 9 + 6 + 8 + 3)^3 = 27^3 is the largest such number.
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
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REFERENCES
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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)
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LINKS
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FORMULA
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EXAMPLE
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4913 = (4 + 9 + 1 + 3)^3.
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MATHEMATICA
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Select[Range[20000], Total[IntegerDigits[#]]^3==#&] (* Harvey P. Dale, Apr 11 2015 *)
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PROG
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(PARI) for(n=0, 999999, sumdigits(n)^3==n&&print1(n", ")) \\ M. F. Hasler, Apr 12 2015
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CROSSREFS
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KEYWORD
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nonn,fini,full,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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