A343680 Niven (or Harshad) numbers which when divided by sum of their digits, give a quotient which is a Zuckerman number.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 18, 21, 24, 27, 36, 42, 45, 48, 54, 63, 72, 81, 84, 108, 135, 198, 216, 324, 648, 1008, 1035, 1050, 1152, 1215, 1344, 1380, 1680, 1725, 2016, 2376, 2592, 2625, 2688, 2997, 3675, 3816, 3888, 5616, 5670, 6912, 10008, 10017, 10035, 10044

Offset

1,2

Comments

The first 24 terms of A114440 are the first 24 terms of this sequence, then A114440(25) = 162, while a(25) = 135.

Links

Table of n, a(n) for n=1..54.

Giovanni Resta, Zuckerman Numbers, Numbers Aplenty.

Example

84 is a Niven number as 84/(8+4) = 7, 7/7 = 1 so 7 is a Zuckerman number, and 84 is a term.
108 is a Niven number as 108/(1+0+8) = 12, 12/(1*2) = 6 so 12 is a Zuckerman number, and 108 is a term.

Mathematica

zuckQ[n_] := IntegerQ[n] && (prod = Times @@ IntegerDigits[n]) > 0 && Divisible[n, prod]; Select[Range[10^4], zuckQ[#/Plus @@ IntegerDigits[#]] &] (* Amiram Eldar, Apr 26 2021 *)

Prog

(PARI) isz(n) = my(p=vecprod(digits(n))); p && !(n % p); \\ A007602
isok(n) = my(s=sumdigits(n)); !(n%s) && isz(n/s); \\ Michel Marcus, Apr 26 2021

Crossrefs

Cf. A005349, A007602, A114440, A235507.

Sequence in context: A079042 A193455 A356349 * A114440 A334416 A217973

Adjacent sequences: A343677 A343678 A343679 * A343681 A343682 A343683

Keyword

nonn,base

Author

Bernard Schott, Apr 26 2021

Extensions

More terms from Michel Marcus, Apr 26 2021

Status

approved