A085648 Brilliant numbers (A078972) whose digital sum is also brilliant.

4, 6, 9, 15, 121, 253, 361, 437, 451, 473, 527, 671, 703, 799, 851, 901, 923, 979, 1003, 1027, 1067, 1081, 1139, 1157, 1207, 1247, 1261, 1333, 1513, 1517, 1643, 1711, 2183, 2291, 2701, 2813, 3007, 3403, 3551, 3589, 3713, 4307, 4399, 4489, 5041, 5063, 5767

Offset: 1

Author

Amarnath Murthy, Jason Earls, Jul 11 2003

Keywords

• base
• nonn

Examples

			7470269 is a term because 7470269 = 1249*5981 and 7+4+7+0+2+6+9 = 35 = 5*7.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A078972.

Programs

Maple

isbril:= proc(n) local F;
  F:= ifactors(n)[2];
  (nops(F)=1 and F[1][2]=2) or (nops(F)=2 and F[1][2]=1 and F[2][2]=1 and ilog10(F[1][1])=ilog10(F[2][1]))
end proc:
R:= NULL:
for d from 1 to 2 do
  if d = 1 then P:= [2,3,5,7]
  else P:= select(isprime, [seq(i,i=10^(d-1)+1..10^d-1,2)])
  fi;
  R:= R, op(sort(select(t -> isbril(convert(convert(t,base,10),`+`)), [seq(seq(P[i]*P[j],j=1..i),i=1..nops(P))])))
od:
R; # Robert Israel, Nov 24 2020

Extensions

Offset changed by Robert Israel, Nov 24 2020