Search: id:A006753
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%I A006753 M3582
%S A006753 4,22,27,58,85,94,121,166,202,265,274,319,346,355,378,382,391,438,
%T A006753 454,483,517,526,535,562,576,588,627,634,636,645,648,654,663,666,
%U A006753 690,706,728,729,762,778,825,852,861,895,913,915,922,958,985,1086
%N A006753 Smith (or joke) numbers: composite numbers n such that sum of digits 
               of n = sum of digits of prime factors of n (counted with multiplicity).
%C A006753 Of course primes also have this property, trivially.
%D A006753 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006753 M. Gardner, Penrose Tiles to Trapdoor Ciphers. Freeman, NY, 1989, p. 
               300.
%D A006753 R. K. Guy, Unsolved Problems in the Theory of Numbers, Section B49.
%D A006753 Oltikar, Sham and Keith Wayland. "Construction of Smith Numbers," Mathematics 
               Magazine, vol. 56(1), 1983, pp. 36-37.
%D A006753 C. A. Pickover, "A Brief History of Smith Numbers" in "Wonders of Numbers: 
               Adventures in Mathematics, Mind and Meaning", pp. 247-248, Oxford 
               University Press, 2000.
%D A006753 J. E. Roberts, Lure of the Integers, pp. 269-270 MAA 1992.
%D A006753 D. D. Spencer, Key Dates in Number Theory History, pp. 94. Camelot Pub. 
               Co. FL, 1995.
%D A006753 David Wells, The Penguin Dictionary of Curious and Interesting Numbers 
               (Rev. ed. 1997), p. 180.
%D A006753 A. Wilansky, Smith numbers, Two-Year Coll. Math. J., 13 (1982), 21.
%H A006753 T. D. Noe, <a href="b006753.txt">Table of n, a(n) for n=1..10000</a>
%H A006753 K. S. Brown's Mathpages, <a href="http://www.mathpages.com/home/kmath007/
               kmath007.htm">Smith Numbers and Rhonda Numbers</a>
%H A006753 C. K. Caldwell, The Prime Glossary, <a href="http://primes.utm.edu/glossary/
               page.php?sort=SmithNumber">Smith number</a>
%H A006753 P. J. Costello, <a href="http://www.math.eku.edu/PJCostello/smith.htm">
               Smith Numbers</a>
%H A006753 S. S. Gupta, <a href="http://www.shyamsundergupta.com/smith.htm">Smith 
               Numbers</a>
%H A006753 Madras Math's Amazing Number Facts, <a href="http://www.users.zetnet.co.uk/
               madras/maths/amazingnofacts/fact042.html">Smith Numbers</a>
%H A006753 C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind 
               and Meaning," <a href="http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?first=1&maxdocs=3&type=html&an\
               =0983.00008&format=complete">Zentralblatt review</a>
%H A006753 C. Riveras, PrimePuzzles.Net, <a href="http://www.primepuzzles.net/puzzles/
               puzz_107.htm">Problem 107:Consecutive Smith numbers</a>
%H A006753 C. Riveras, PrimePuzzles.Net, <a href="http://www.primepuzzles.net/puzzles/
               puzz_108.htm">Problem 108:Methods for generating Smith numbers</a>
%H A006753 W. Schneider, <a href="http://www.wschnei.de/digit-related-numbers/smith-numbers.html">
               Smith Numbers</a>
%H A006753 Jason T., <a href="http://everything2.net/index.pl?node_id=1104442&displaytype=printable&lastnode_id=1104442"\
               >Smith number</a>
%H A006753 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SmithNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A006753 Wikipedia, <a href="http://en.wikipedia.org/wiki/Smith_number">Smith 
               number</a>
%e A006753 58=2*29, 58->13, 2->2, 29->11 and indeed 13=2+11.
%Y A006753 Cf. A019506.
%Y A006753 Cf. A050224, A050255, A098834-A098840, A103123-A103126, A104166-A104171, 
               A104390, A104391.
%Y A006753 Sequence in context: A009925 A059653 A022385 this_sequence A098836 A036920 
               A036921
%Y A006753 Adjacent sequences: A006750 A006751 A006752 this_sequence A006754 A006755 
               A006756
%K A006753 nonn,base,nice,easy
%O A006753 1,1
%A A006753 N. J. A. Sloane (njas(AT)research.att.com).

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