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A178158 Numbers n that are divisible by every suffix of n. 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A034838 A063527 A209933

Adjacent sequences:  A178155 A178156 A178157 * A178159 A178160 A178161

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Dec 17 2010

STATUS

approved

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Last modified October 18 17:13 EDT 2019. Contains 328186 sequences. (Running on oeis4.)