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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 * A367956 A371603 A248656
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 June 16 02:19 EDT 2024. Contains 373416 sequences. (Running on oeis4.)