A178157 Numbers k that are divisible by every prefix of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30, 33, 36, 39, 40, 44, 48, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 330, 360, 390, 400, 420, 440, 460, 480, 500, 510, 520, 530, 540, 550, 560

Offset: 1

Author

Michel Lagneau, Dec 17 2010

Keywords

• nonn
• base

Examples

			3570 is in the sequence because:
     3 | 3570;
    35 | 3570;
   357 | 3570;
  3570 | 3570.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A034837.

Programs

Maple

with(numtheory):T:=array(1..9):for n from 1 to 10000 do:ind:=0:l:=length(n):n0:=n:s:=0:for
  m from 1 to l do:q:=n0:u:=irem(q,10):v:=iquo(q,10):n0:=v :T[m]:=u:od:for i from
  1 to l do: s1:=0:for j from 0 to i-1 do: s1:=s1 + T[l-i+j+1]*10^j :od:if irem(n,s1)=0
  then ind:=ind+1:else fi:od:if ind=l then printf(`%d, `,n):else fi:od:

Mathematica

Select[Range[560],AllTrue[Table[Boole[Divisible[#,Floor[#/10^i]]],{i,0,Log10[#]}],Positive] &] (* Stefano Spezia, May 03 2025 *)