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

%I A272436 #35 Feb 15 2018 08:14:04
%S A272436 4,6,9,22,123,213,321,1142,1214,1241,4121,11215,11521,12115,12151,
%T A272436 21151,22121,51211,111261,112611,116121,116211,121161,162111,211611,
%U A272436 261111,621111,1111217,1111413,1111431,1111721,1112117,1117121,1117211,1121117,1121171,1121711
%N A272436 Semiprimes such that sum of digits equals product of digits.
%C A272436 Intersection of A001358 and A034710.
%C A272436 9 is the only member with digit 9. No member has more than one digit 3 or 6. - _Robert Israel_, May 06 2016
%H A272436 Chai Wah Wu, <a href="/A272436/b272436.txt">Table of n, a(n) for n = 1..17009</a> (n = 1..3104 from Robert Israel)
%e A272436 1142 appears in the list because 1142 = 2*571 that is semiprime. Also, 1+1+4+2 = 8 = 1*1*4*2.
%e A272436 11215 appears in the list because 1142 = 5*2243 that is semiprime. Also, 1+1+2+1+5 = 10 = 1*1*2*1*5.
%p A272436 R:= proc(k,d,u,v) option remember;
%p A272436     if k = 1 then
%p A272436         if d = v - u then {[d]}
%p A272436         else {}
%p A272436         fi
%p A272436     else
%p A272436       `union`(seq(map(t -> [op(t),s], procname(k-1,d-s,u+s*k,v*k^s)),s=0..d))
%p A272436     fi
%p A272436 end proc:
%p A272436 A034710:= proc(d)
%p A272436   local res, r,  i, t;
%p A272436   res:= NULL;
%p A272436   for r in R(9,d,0,1) do
%p A272436      res:= res, op(map(t -> add(10^(i-1)*t[i],i=1..nops(t)), combinat:-permute([seq(i$r[i],i=1..9)])));
%p A272436   od:
%p A272436   sort([res]);
%p A272436 end proc:
%p A272436 map(op, [seq(select(t -> numtheory:-bigomega(t)=2, A034710(i)),i=1..11)]); # _Robert Israel_, May 06 2016
%t A272436 Select[Range[10000000], (Plus @@ IntegerDigits[#]) == (Times @@ IntegerDigits[#]) && PrimeOmega[#] == 2 &]
%Y A272436 Cf. A001358, A034710, A066306, A066307.
%K A272436 nonn,base
%O A272436 1,1
%A A272436 _K. D. Bajpai_, May 06 2016