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

1,2

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

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

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

Intersection of A005349 and A055471.

Supersequence of A038186.

Cf. A051004, A328273, A342650.

Sequence in context: A365420 A342650 A328273 * A255734 A357142 A033075

Adjacent sequences: A342259 A342260 A342261 * A342263 A342264 A342265

Keyword

nonn,base

Author

Bernard Schott, Mar 27 2021

Extensions

Example clarified by Harvey P. Dale, Sep 26 2021

Status

approved