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 A050225 #30 Mar 13 2025 12:11:48 %S A050225 6969,19998,36399,39693,66099,69663,69897,89769,99363,99759,109989, %T A050225 118899,181998,191799,199089,297099,306939,333399,336963,339933, %U A050225 363099,396363,397998,399333,399729,588969,606666,606909,639633,660693,666633 %N A050225 1/3-Smith numbers. %H A050225 Amiram Eldar, <a href="/A050225/b050225.txt">Table of n, a(n) for n = 1..10000</a> %H A050225 Shyam Sunder Gupta, <a href="http://www.shyamsundergupta.com/smith.htm">Smith Numbers</a>. %H A050225 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_4">Smith Numbers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 4, 127-157. %H A050225 Wayne L. McDaniel, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/25-1/mcdaniel.pdf">The Existence of infinitely Many k-Smith numbers</a>, Fibonacci Quarterly, Vol. 25, No. 1 (1987), pp. 76-80. %H A050225 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmithNumber.html">Smith Numbers</a>. %e A050225 6969 is a 3^(-1) Smith number because the digit sum of 6969, i.e., S(6969) = 6 + 9 + 6 + 9 = 30, which is equal to 3 times the sum of the digits of its prime factors, i.e., 3*Sp(6969) = 3 * Sp(3 * 23 * 101) = 3 *( 3 + 2 + 3 + 1 + 0 + 1) = 30. %t A050225 digSum[n_] := Plus @@ IntegerDigits[n]; thirdSmithQ[n_] := CompositeQ[n] && 3 * Plus @@ (Last@# * digSum[First@#] & /@ FactorInteger[n]) == digSum[n]; Select[Range[666633], thirdSmithQ] (* _Amiram Eldar_, Aug 23 2020 *) %Y A050225 Cf. A006753, A050224. %K A050225 nonn,base %O A050225 1,1 %A A050225 _Eric W. Weisstein_ %E A050225 More terms from _Shyam Sunder Gupta_, Mar 11 2005