A351618 Numbers that are both Zuckerman numbers and Smith numbers.

4, 1111, 3168, 7119, 31488, 141184, 698112, 1169316, 1621248, 1687392, 1938816, 1967112, 12469248, 12822912, 14112672, 16616448, 41484288, 79817472, 116149248, 121911264, 128894976, 163319328, 166491936, 193916916, 218431488, 247984128, 798142464, 817883136

Offset

1,1

Links

Table of n, a(n) for n=1..28.

Giovanni Resta, Smith numbers, Numbers Aplenty.

Giovanni Resta, Zuckerman numbers, Numbers Aplenty.

Example

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).

Mathematica

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 *)

Prog

(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

Crossrefs

Intersection of A007602 and A006753.

Cf. A334527.

Sequence in context: A159859 A110499 A009013 * A367956 A371603 A248656

Adjacent sequences: A351615 A351616 A351617 * A351619 A351620 A351621

Keyword

nonn,base

Author

Bernard Schott, Feb 15 2022

Extensions

More terms from Amiram Eldar, Feb 15 2022

Status

approved