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A272436
Semiprimes such that sum of digits equals product of digits.
2
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
1,1
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
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..17009 (n = 1..3104 from Robert Israel)
EXAMPLE
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.
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 &]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
K. D. Bajpai, May 06 2016
STATUS
approved