%I #28 Feb 16 2022 10:35:16
%S 4,1111,3168,7119,31488,141184,698112,1169316,1621248,1687392,1938816,
%T 1967112,12469248,12822912,14112672,16616448,41484288,79817472,
%U 116149248,121911264,128894976,163319328,166491936,193916916,218431488,247984128,798142464,817883136
%N Numbers that are both Zuckerman numbers and Smith numbers.
%H Giovanni Resta, <a href="https://www.numbersaplenty.com/set/Smith_number/">Smith numbers</a>, Numbers Aplenty.
%H Giovanni Resta, <a href="https://www.numbersaplenty.com/set/Zuckerman_number/">Zuckerman numbers</a>, Numbers Aplenty.
%e 3168 is a term since it is a Zuckerman number (3*1*6*8) = 144 is a divisor of 3168 and a Smith number (3168 = 2*2*2*2*2*3*3*11 and 2+2+2+2+2+3+3+1+1 = 3+1+6+8).
%t digSum[n_] := Plus @@ IntegerDigits[n]; smithQ[n_] := CompositeQ[n] && Plus @@ (Last@# * digSum[First@#] & /@ FactorInteger[n]) == digSum[n]; zuckQ[n_] := (prodig = Times @@ IntegerDigits[n]) > 0 && Divisible[n, prodig]; Select[Range[10^6], zuckQ[#] && smithQ[#] &] (* _Amiram Eldar_, Feb 15 2022 *)
%o (PARI) isok(m) = my(d=digits(m)); if (vecmin(d) && !(m % vecprod(d)) && !isprime(m) , my(f=factor(m)); sum(k=1, #f~, sumdigits(f[k,1])*f[k,2]) == vecsum(d)); \\ _Michel Marcus_, Feb 15 2022
%Y Intersection of A007602 and A006753.
%Y Cf. A334527.
%K nonn,base
%O 1,1
%A _Bernard Schott_, Feb 15 2022
%E More terms from _Amiram Eldar_, Feb 15 2022