A342855 Numbers that contain a digit 0 (A011540) and that are divisible by their nonzero digits (A002796).

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 102, 104, 105, 110, 120, 140, 150, 200, 202, 204, 208, 210, 220, 240, 250, 280, 300, 303, 306, 330, 360, 400, 404, 408, 420, 440, 480, 500, 505, 510, 520, 540, 550, 600, 606, 630, 660, 700, 707, 770, 800, 808, 840, 880, 900, 909, 990, 1000

Offset: 1

Author

Bernard Schott, Mar 25 2021

Keywords

• nonn
• base

Comments

If m is a term, so is 10*m.

Examples

			208 = 2*104 = 8*26 is divisible by 2 and divisible by 8, 208 contains a digit 0, hence 208 is a term.
		

Links

• Index entries for 10-automatic sequences.

Crossrefs

Intersection of A002796 and A011540.

Programs

Mathematica

q[n_] := MemberQ[(d = IntegerDigits[n]), 0] && AllTrue[d, # == 0 || Divisible[n, #] &]; Select[Range[1000], q] (* Amiram Eldar, Mar 25 2021 *)

PARI

isok(m) = my(d=digits(m)); if (vecmin(d), return (0)); d = vecsort(select(x->(x > 0), d),,8); for (k=1, #d, if (m % d[k], return(0))); return(1); \\ Michel Marcus, Mar 29 2021

Formula

a(n) ~ 2520n. - Charles R Greathouse IV, Nov 25 2024