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 A351618 Numbers that are both Zuckerman numbers and Smith numbers. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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 * A248656 A357512 A309979 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

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Last modified February 1 03:45 EST 2023. Contains 359981 sequences. (Running on oeis4.)