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%I #21 Aug 23 2020 02:09:51
%S 2401,5010,7000,10005,10311,10410,10411,11060,11102,11203,12103,13002,
%T 13021,13101,14001,14101,14210,20022,20121,20203,20401,21103,21112,
%U 21120,21201,22040,22101,22201,23030,30003,30031,30320,31002,31101
%N 4-Smith numbers.
%H Amiram Eldar, <a href="/A103125/b103125.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..600 from Harvey P. Dale)
%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 2401 is a 4-Smith number because the sum of the digits of its prime factors, i.e., Sp(2401) = Sp(7*7*7*7) = 7 + 7 + 7 + 7 = 28, which is equal to 4 times the digit sum of 2401, i.e., 4*S(2401) = 4*(2 + 4 + 0 + 1) = 28.
%t sn4Q[n_]:=Module[{a=Total[Flatten[IntegerDigits/@(Table[First[#],{Last[ #]}]&/@FactorInteger[n])]],b=4Total[IntegerDigits[n]]},a==b] (* _Harvey P. Dale_, Oct 03 2011 *)
%Y Cf. A006753.
%K base,nonn
%O 1,1
%A _Shyam Sunder Gupta_, Mar 16 2005
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