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A046459 Dudeney numbers: integers equal to the sum of the digits of their cubes.

%I A046459 #69 Feb 16 2025 08:32:39
%S A046459 0,1,8,17,18,26,27
%N A046459 Dudeney numbers: integers equal to the sum of the digits of their cubes.
%C A046459 This sequence was first found by the French mathematician Claude (Séraphin) Moret-Blanc in 1879. See Le Lionnais page 27 for the last term of this sequence: 27. - _Bernard Schott_, Dec 07 2012
%C A046459 The name "Dudeney numbers" appears in the October 2018 issue of Mathematics Teacher (see link). - _N. J. A. Sloane_, Oct 10 2018
%D A046459 H. E. Dudeney, 536 Puzzles & Curious Problems, reprinted by Souvenir Press, London, 1968, p. 36, #120.
%D A046459 Italo Ghersi, Matematica dilettevole e curiosa, p. 115, Hoepli, Milano, 1967. [From _Vincenzo Librandi_, Jan 02 2009]
%D A046459 F. Le Lionnais, Les nombres remarquables, Hermann, 1983.
%D A046459 J. Roberts, Lure of the Integers, The Mathematical Association of America, 1992, p. 172.
%D A046459 David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 96.
%H A046459 H. E. Dudeney, <a href="https://archive.org/details/isbn_9780684310329/page/36/mode/1up">536 Puzzles & Curious Problems</a>.
%H A046459 The Mathematics Teacher, <a href="https://doi.org/10.5951/mathteacher.112.2.0120">October 2018 Calendar and Solutions</a>, Volume 112, Number 2, October 2018, pages 120 and 122.
%H A046459 ProofWiki, <a href="https://proofwiki.org/wiki/Sequence_of_Dudeney_Numbers">Sequence of Dudeney Numbers</a>.
%H A046459 Bernard Schott and Norbert Verdier, <a href="http://www.les-mathematiques.net/phorum/read.php?17,493170">QDL 19: Quels beaux cubes!</a> (French mathematical forum les-mathematiques.net).
%H A046459 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>.
%e A046459 a(3) = 8 because 8^3 = 512 and 5 + 1 + 2 = 8.
%e A046459 a(7) = 27 because 27^3 = 19683 and 1 + 9 + 6 + 8 + 3 = 27.
%t A046459 Select[Range[0,30],#==Total[IntegerDigits[#^3]]&] (* _Harvey P. Dale_, Dec 21 2014 *)
%o A046459 (Magma) [n: n in [0..100] | &+Intseq(n^3) eq n ]; // _Vincenzo Librandi_, Sep 16 2015
%o A046459 (Python) a = [n for n in range(100) if sum(map(int, str(n ** 3))) == n] # _David Radcliffe_, Aug 18 2022
%o A046459 (PARI) isok(k)=sumdigits(k^3)==k \\ _Patrick De Geest_, Dec 10 2024
%Y A046459 Cf. A004164, A055569, A055575, A055576, A055577.
%Y A046459 Cf. A152147.
%K A046459 base,fini,full,nonn
%O A046459 1,3
%A A046459 _Patrick De Geest_, Aug 15 1998
%E A046459 Offset corrected by _Arkadiusz Wesolowski_, Aug 09 2013