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

1,2

Comments

Repunit R(k) is a term iff k divides R(k) (A014950).

Links

Table of n, a(n) for n=1..49.

Giovanni Resta, Zuckerman numbers, Numbers Aplenty.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A005349, A007602, A235507, A288069, A343680, A343681.

Sequence in context: A185186 A336580 A115569 * A343744 A064653 A130588

Adjacent sequences: A343679 A343680 A343681 * A343683 A343684 A343685

Keyword

nonn,base

Author

Bernard Schott, Apr 26 2021

Extensions

More terms from Michel Marcus, Apr 26 2021

Status

approved