A202388 Digital root of Smith numbers A006753.

4, 4, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 6, 4, 6, 4, 4, 4, 4, 9, 3, 6, 4, 6, 6, 9, 6, 6, 9, 6, 4, 8, 9, 6, 4, 6, 6, 6, 4, 4, 6, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 8, 9, 4, 6, 6, 4, 4, 4, 8, 9, 3, 4, 4, 6, 4, 9, 9, 4, 4, 9, 4, 9, 8, 9, 4, 4, 6, 9, 4, 4

Offset: 1

Author

Reinhard Zumkeller, Dec 19 2011

Keywords

• nonn
• base

Comments

a(n) = A010888(A006753(n)); range = {4,6,8,9}.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Smith Number
• Wikipedia, Smith number

Crossrefs

Cf. A050218, A202393.

Programs

Mathematica

d[n_]:=IntegerDigits[n]; dr[n_]:= NestWhile[Total[d[#]]&,n,#>9&]; tr[n_]:=Transpose[FactorInteger[n]]; t1=Select[Range[4,2.2*10^3],!PrimeQ[#]&&Total[d[#]]==Total[d@tr[#][[1]]*tr[#][[2]],2]&]; Table[dr[n],{n,t1}] (* t1 gives Smith numbers - Jayanta Basu, Jun 04 2013 *)