

A343680


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


2



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
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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



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



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



