A178158 Numbers n that are divisible by every suffix of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 21, 22, 24, 25, 31, 32, 33, 35, 36, 41, 42, 44, 45, 48, 51, 52, 55, 61, 62, 63, 64, 65, 66, 71, 72, 75, 77, 81, 82, 84, 85, 88, 91, 92, 93, 95, 96, 99, 101, 102, 104, 105, 125, 201, 202, 204, 205, 208, 225, 301, 302, 303, 304, 305, 306, 312, 315, 325, 375, 401, 402, 404, 405, 408, 425, 501, 502, 504, 505, 525, 601, 602, 603, 604

Offset

1,2

Comments

If n = y*10^d+z is in the sequence, where 1<=y<=9 and z < 10^d, then z | y*10^d. - Robert Israel, Oct 17 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000 (first 788 terms from Reinhard Zumkeller)

Math Overflow, The number of numbers no greater than n that are divisible by all their suffixes

Example

9375 is in the sequence because :
.     5 | 9375 ;
.    75 | 9375 ;
.   375 | 9375 ;
.  9375 | 9375 .

Maple

with(numtheory):T:=array(1..5):for n from 1 to 10000 do:ind:=0:l:=length(n):n0:=n:s:=0:for m from 0 to l-1 do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v : s:=s + u*10 ^m:if irem(n, 10)<>0 and irem(n, s)=0 then ind:=ind+1:else fi:od:if ind=l then printf(`%d, `, n):else fi:od:
# Alternative:
filter:= proc(x)
  if x mod 10 = 0 then return false fi;
  andmap(t -> type(x/(x mod 10^t), integer), [$1..ilog10(x)])
end proc:
Res:= $1..9:
for d from 1 to 6 do
  for y from 1 to 9 do
    for z in sort(convert(select(`<`, numtheory:-divisors(y*10^d), 10^d), list)) do
      if filter(y*10^d+z) then
         Res:= Res, y*10^d+z;
      fi
od od od:
Res; # Robert Israel, Oct 17 2018

Prog

(Haskell)
import Data.List (tails)
a178158 n = a178158_list !! (n-1)
a178158_list = filter (\suff -> all ((== 0) . (mod suff))
   (map read $ tail $ init $ tails $ show suff :: [Integer])) a067251_list
-- Reinhard Zumkeller, Mar 26 2012

Crossrefs

Cf. A034709 .

Cf. A067251.

Sequence in context: A084433 A084434 A034709 * A337184 A034838 A063527

Adjacent sequences: A178155 A178156 A178157 * A178159 A178160 A178161

Keyword

nonn,base

Author

Michel Lagneau, Dec 17 2010

Status

approved