This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A351618 #28 Feb 16 2022 10:35:16 %S A351618 4,1111,3168,7119,31488,141184,698112,1169316,1621248,1687392,1938816, %T A351618 1967112,12469248,12822912,14112672,16616448,41484288,79817472, %U A351618 116149248,121911264,128894976,163319328,166491936,193916916,218431488,247984128,798142464,817883136 %N A351618 Numbers that are both Zuckerman numbers and Smith numbers. %H A351618 Giovanni Resta, <a href="https://www.numbersaplenty.com/set/Smith_number/">Smith numbers</a>, Numbers Aplenty. %H A351618 Giovanni Resta, <a href="https://www.numbersaplenty.com/set/Zuckerman_number/">Zuckerman numbers</a>, Numbers Aplenty. %e A351618 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 A351618 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 A351618 (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 A351618 Intersection of A007602 and A006753. %Y A351618 Cf. A334527. %K A351618 nonn,base %O A351618 1,1 %A A351618 _Bernard Schott_, Feb 15 2022 %E A351618 More terms from _Amiram Eldar_, Feb 15 2022