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%I #27 Aug 24 2020 08:52:29
%S 402,510,700,1113,1131,1311,2006,2022,2130,2211,2240,3102,3111,3204,
%T 3210,3220,4031,4300,4410,5310,6004,6100,6300,7031,7120,9000,10034,
%U 10125,10206,10251,10304,10413,10521,10612,10800,11033,11111,11114,11116,11121,11141
%N 3-Smith numbers.
%H Amiram Eldar, <a href="/A104391/b104391.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1500 from G. C. Greubel)
%H Shyam Sunder Gupta, <a href="http://www.shyamsundergupta.com/smith.htm">Smith numbers</a>.
%H Wayne L. McDaniel, <a href="http://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.
%e 402 is a 3-Smith number because the sum of the digits of its prime factors, i.e., Sp(402) = Sp(2*3*67)= 2 + 3 + 6 + 7 = 18, which is equal to 3 times the digit sum of 402, i.e., 3*S(402) = 3*(4 + 0 + 2) = 18.
%t Select[Range[12000],Total[Flatten[IntegerDigits/@Table[#[[1]],{#[[2]]}]&/@ FactorInteger[#]]]/Total[IntegerDigits[#]]==3&] (* _Harvey P. Dale_, Feb 19 2013 *)
%Y Cf. A006753, A104390.
%K nonn,base
%O 1,1
%A _Eric W. Weisstein_, Mar 04 2005 and _Shyam Sunder Gupta_, Mar 11 2005
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