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 A061209 Numbers which are the cubes of their digit sum. 12
 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, 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 Cf. A007953, A061210, A061211, A252648. Sequence in context: A186845 A239917 A114287 * A017259 A017367 A254899 Adjacent sequences:  A061206 A061207 A061208 * A061210 A061211 A061212 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 November 25 05:43 EST 2020. Contains 338617 sequences. (Running on oeis4.)