A272436 Semiprimes such that sum of digits equals product of digits.

4, 6, 9, 22, 123, 213, 321, 1142, 1214, 1241, 4121, 11215, 11521, 12115, 12151, 21151, 22121, 51211, 111261, 112611, 116121, 116211, 121161, 162111, 211611, 261111, 621111, 1111217, 1111413, 1111431, 1111721, 1112117, 1117121, 1117211, 1121117, 1121171, 1121711

Offset: 1

Author

K. D. Bajpai, May 06 2016

Keywords

• nonn
• base

Comments

Intersection of A001358 and A034710.

9 is the only member with digit 9. No member has more than one digit 3 or 6. - Robert Israel, May 06 2016

Examples

			1142 appears in the list because 1142 = 2*571 that is semiprime. Also, 1+1+4+2 = 8 = 1*1*4*2.
11215 appears in the list because 1142 = 5*2243 that is semiprime. Also, 1+1+2+1+5 = 10 = 1*1*2*1*5.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..17009 (n = 1..3104 from Robert Israel)

Crossrefs

Cf. A001358, A034710, A066306, A066307.

Programs

Maple

R:= proc(k,d,u,v) option remember;
    if k = 1 then
        if d = v - u then {[d]}
        else {}
        fi
    else
      `union`(seq(map(t -> [op(t),s], procname(k-1,d-s,u+s*k,v*k^s)),s=0..d))
    fi
end proc:
A034710:= proc(d)
  local res, r,  i, t;
  res:= NULL;
  for r in R(9,d,0,1) do
     res:= res, op(map(t -> add(10^(i-1)*t[i],i=1..nops(t)), combinat:-permute([seq(i$r[i],i=1..9)])));
  od:
  sort([res]);
end proc:
map(op, [seq(select(t -> numtheory:-bigomega(t)=2, A034710(i)),i=1..11)]); # Robert Israel, May 06 2016

Mathematica

Select[Range[10000000], (Plus @@ IntegerDigits[#]) == (Times @@ IntegerDigits[#]) && PrimeOmega[#] == 2 &]