%I #13 Apr 22 2021 18:06:51
%S 4,22,666,1111,6666666,4444444444,44444444444444444444,
%T 555555555555555555555555555,55555555555555555555555555555555,
%U 4444444444444444444444444444444444444444444444444444444
%N Repdigit Smith numbers.
%H S. S. Gupta, <a href="http://www.shyamsundergupta.com/smith.htm">Smith Numbers</a>.
%t d[n_]:=IntegerDigits[n]; tr[n_]:=Transpose[FactorInteger[n]]; a[n_]:=NestList[FromDigits[Flatten[d[{#,n}]]]&,n,55]; t={}; Do[If[!PrimeQ[n]&&Total[d[n]]==Total[d@tr[n][[1]]*tr[n][[2]],2],AppendTo[t,n]],{n,Drop[Union[Flatten[Table[a[k],{k,9}]]],1]}]; t (* _Jayanta Basu_, Jun 04 2013 *)
%o (Python)
%o from sympy import factorint
%o from itertools import product
%o def sd(n): return sum(map(int, str(n)))
%o def smith(n):
%o f = factorint(n)
%o return sum(f[p] for p in f) > 1 and sd(n) == sum(sd(p)*f[p] for p in f)
%o def repsto(limit):
%o yield from range(min(limit, 9)+1)
%o for rep in range(2, 10**len(str(limit))):
%o for digit in "123456789":
%o out = int(digit*rep)
%o if out > limit: return
%o yield out
%o print(list(filter(smith, repsto(10**32)))) # _Michael S. Branicky_, Apr 22 2021
%Y Cf. A006753.
%Y Subsequence of both A098834 and A104171.
%K base,nonn
%O 1,1
%A _Shyam Sunder Gupta_, Mar 10 2005
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