

A342262


Numbers divisible both by the product of their nonzero digits (A055471) and by the sum of their digits (A005349).


2



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 20, 24, 30, 36, 40, 50, 60, 70, 80, 90, 100, 102, 110, 111, 112, 120, 132, 135, 140, 144, 150, 200, 210, 216, 220, 224, 240, 300, 306, 312, 315, 360, 400, 432, 480, 500, 510, 540, 550, 600, 612, 624, 630, 700, 735, 800, 900, 1000, 1002, 1008
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OFFSET

1,2


COMMENTS

Equivalently, Niven numbers that are divisible by the product of their nonzero digits. A Niven number (A005349) is a number that is divisible by the sum of its digits.
Niven numbers without zero digit that are divisible by the product of their digits are in A038186.
Differs from super Niven numbers, the first 16 terms are the same, then A328273(17) = 48 while a(17) = 50.
This sequence is infinite since if m is a term, then 10*m is another term.


LINKS



EXAMPLE

The product of the nonzero digits of 306 = 3*6 = 18, and 306 divided by 18 = 17. The sum of the digits of 306 = 3 + 0 + 6 = 9, and 306 divided by 9 = 34. Thus 306 is a term.


MATHEMATICA

q[n_] := And @@ Divisible[n, {Times @@ (d = Select[IntegerDigits[n], # > 0 &]), Plus @@ d}]; Select[Range[1000], q] (* Amiram Eldar, Mar 27 2021 *)
Select[Range[1200], Mod[#, Times@@(IntegerDigits[#]/.(0>1))]== Mod[#, Total[ IntegerDigits[#]]]==0&] (* Harvey P. Dale, Sep 26 2021 *)


PROG

(PARI) isok(m) = my(d=select(x>(x!=0), digits(m))); !(m % vecprod(d)) && !(m % vecsum(d)); \\ Michel Marcus, Mar 27 2021


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



