A342262 Numbers divisible both by the product of their nonzero digits (A055471) and by the sum of their digits (A005349).

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

Offset: 1

Author

Bernard Schott, Mar 27 2021

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A005349 and A055471.

Supersequence of A038186.

Cf. A051004, A328273, A342650.

Programs

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 *)

PARI

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

Extensions

Example clarified by Harvey P. Dale, Sep 26 2021