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%I #39 Mar 03 2023 09:28:24
%S 1,81,1458,1729
%N Numbers n such that n = digit_sum(n)*R(digit_sum(n)) where digit_sum is the sum of digits and R is the digit reversal.
%C These are special Harshad (or Niven) numbers from A005349. They are mentioned in Simon Singh's book "The Simpsons and their Mathematical Secrets", 2013, Bloomsbury, New York (in the German version "Homers letzter Satz", Hanser, 2013, on p. 238). - _Wolfdieter Lang_, Feb 05 2014
%D Tricky Number, Science Illustrated, Jan/Feb 2009, page 80.
%D P. Odifreddi, Il museo dei numeri, Rizzoli, 2014, page 284.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Masahiko_Fujiwara">Masahiko Fujiwara</a>
%F k such that A007953(k)*A004086(A007953(k)) = k. - _Jonathan Vos Post_, Dec 20 2008
%e n = 1729: s = 1 + 7 + 2 + 9 = 19, 19*91 = 1729.
%t dsrQ[n_]:=Module[{c=Total[IntegerDigits[n]]},c IntegerReverse[c]==n]; Select[Range[ 2000],dsrQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 19 2020 *)
%o #!/usr/bin/perl -w use strict; my $i; my $j; for $i ( 1e0 .. 1e6 ) { my $sum = 0; my $rev = 0; for $j ( 1 .. length ( $i ) ) { $sum += substr ( $i, $j - 1, 1 ); } $rev = reverse $sum; print "$i " if $sum * $rev == $i; }
%Y Cf. A004086, A007953.
%K nonn,base,fini,full
%O 1,2
%A Michael Vang (michael.vang(AT)gmail.com), Sep 22 2005
%E Edited by _N. J. A. Sloane_, Jan 15 2009, at the suggestion of _Klaus Brockhaus_
%E Edited by _Charles R Greathouse IV_, Aug 03 2010
%E Title corrected by _Wolfdieter Lang_, Feb 05 2014
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