This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A061209 #47 May 23 2025 11:06:40 %S A061209 0,1,512,4913,5832,17576,19683 %N A061209 Numbers which are the cubes of their digit sum. %C A061209 It can be shown that 19683 = (1 + 9 + 6 + 8 + 3)^3 = 27^3 is the largest such number. %C A061209 Numbers of Dudeney. - _Philippe Deléham_, May 11 2013 %C A061209 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 A061209 H. E. Dudeney, 536 Puzzles & Curious Problems, Souvenir Press, London, 1966, p. 36, #120. %D A061209 Amarnath Murthy, The largest and the smallest m-th power whose digit sum is the m-th root. (To be published) %D A061209 Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 36. %H A061209 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 A061209 Joseph S. Madachy, <a href="https://www.mathstat.dal.ca/FQ/Scanned/6-1/madachy.pdf">Recreational Mathematics</a>, Fibonacci Quarterly 6:1 (1968), pp. 60-68. %H A061209 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dudeney_number">Dudeney number</a> %F A061209 a(n) = A007953(a(n))^3. - _M. F. Hasler_, Apr 12 2015 %e A061209 4913 = (4 + 9 + 1 + 3)^3. %t A061209 Select[Range[20000],Total[IntegerDigits[#]]^3==#&] (* _Harvey P. Dale_, Apr 11 2015 *) %o A061209 (PARI) for(n=0,999999,sumdigits(n)^3==n&&print1(n",")) \\ _M. F. Hasler_, Apr 12 2015 %Y A061209 Cf. A007953, A061210, A061211, A252648. %K A061209 nonn,fini,full,base %O A061209 1,3 %A A061209 _Amarnath Murthy_, Apr 21 2001 %E A061209 Initial term 0 added by _M. F. Hasler_, Apr 12 2015