A343682 Zuckerman numbers which when divided by the product of their digits, give a quotient which is a Niven (Harshad) number.
1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 24, 36, 111, 128, 135, 144, 175, 216, 315, 384, 432, 672, 735, 1296, 1575, 2916, 11115, 11232, 11664, 12132, 12288, 12312, 13212, 13824, 14112, 16416, 22176, 23112, 23328, 26112, 27216, 31212, 32832, 34272, 34992, 42624, 72128, 77175
Offset: 1
Examples
36 is a Zuckerman number as 36/(3*6) = 2, 2/2 = 1 that is a Niven number, and 36 is a term. 315 is a Zuckerman number as 315/(3*1*5) = 21, 21/(2+1) = 7 that is a Niven number, and 315 is a term.
Links
- Giovanni Resta, Zuckerman numbers, Numbers Aplenty.
Programs
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Mathematica
nivenQ[n_] := IntegerQ[n] && (sum = Plus @@ IntegerDigits[n]) > 0 && Divisible[n, sum]; Select[Range[10^5], (prod = Times @@ IntegerDigits[#]) > 0 && nivenQ[# / prod] &] (* Amiram Eldar, Apr 26 2021 *)
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PARI
isn(n) = !(n%sumdigits(n)); \\ A005349 isz(n) = my(p=vecprod(digits(n))); p && !(n % p); \\ A007602 isok(n) = isz(n) && isn(n/vecprod(digits(n))); \\ Michel Marcus, Apr 26 2021
Extensions
More terms from Michel Marcus, Apr 26 2021
Comments