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%I #41 Nov 05 2020 06:45:38
%S 0,1,512,4913,5832,17576,19683
%N Numbers which are the cubes of their digit sum.
%C It can be shown that 19683 = (1 + 9 + 6 + 8 + 3)^3 = 27^3 is the largest such number.
%C Numbers of Dudeney. - _Philippe Deléham_, May 11 2013
%C 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
%D H. E. Dudeney, 536 Puzzles & Curious Problems, Souvenir Press, London, 1966, p. 36, #120.
%D Amarnath Murthy, The largest and the smallest m-th power whose digit sum is the m-th root. (To be published)
%H Henk Koppelaar and Peyman Nasehpour, <a href="https://arxiv.org/abs/2008.08187">On Hardy's Apology Numbers</a>, arXiv:2008.08187 [math.NT], 2020.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dudeney_number">Dudeney number</a>
%F a(n) = A007953(a(n))^3. - _M. F. Hasler_, Apr 12 2015
%e 4913 = (4 + 9 + 1 + 3)^3.
%t Select[Range[20000],Total[IntegerDigits[#]]^3==#&] (* _Harvey P. Dale_, Apr 11 2015 *)
%o (PARI) for(n=0,999999,sumdigits(n)^3==n&&print1(n",")) \\ _M. F. Hasler_, Apr 12 2015
%Y Cf. A007953, A061210, A061211, A252648.
%K nonn,fini,full,base
%O 1,3
%A _Amarnath Murthy_, Apr 21 2001
%E Initial term 0 added by _M. F. Hasler_, Apr 12 2015
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