A034838 -id:A034838 - cp's OEIS frontend

A007602 Numbers that are divisible by the product of their digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 24, 36, 111, 112, 115, 128, 132, 135, 144, 175, 212, 216, 224, 312, 315, 384, 432, 612, 624, 672, 735, 816, 1111, 1112, 1113, 1115, 1116, 1131, 1176, 1184, 1197, 1212, 1296, 1311, 1332, 1344, 1416, 1575, 1715, 2112, 2144

Offset: 1

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

These are called Zuckerman numbers to base 10. [So-named by J. J. Tattersall, after Herbert S. Zuckerman. - Charles R Greathouse IV, Jun 06 2017] - Howard Berman (howard_berman(AT)hotmail.com), Nov 09 2008
This sequence is a subsequence of A180484; the first member of A180484 that is not a member of A007602 is 1114. - D. S. McNeil, Sep 09 2010
Complement of A188643; A188642(a(n)) = 1; A038186 is a subsequence; A168046(a(n)) = 1: subsequence of A052382. - Reinhard Zumkeller, Apr 07 2011
The terms of n digits in the sequence, for n from 1 to 14, are 9, 5, 20, 40, 117, 285, 747, 1951, 5229, 13493, 35009, 91792, 239791, 628412, 1643144, 4314987. Empirically, the counts seem to grow as 0.858*2.62326^n. - Giovanni Resta, Jun 25 2017
De Koninck and Luca showed that the number of Zuckerman numbers below x is at least x^0.122 but at most x^0.863. - Tomohiro Yamada, Nov 17 2017
The quotients obtained when Zuckerman numbers are divided by the product of their digits are in A288069. - Bernard Schott, Mar 28 2021

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
James J. Tattersall, Elementary Number Theory in Nine Chapters (2005), 2nd Edition, p. 86 (see problems 44-45).

Reinhard Zumkeller and Zak Seidov, Table of n, a(n) for n = 1..10000
Jean-Marie De Koninck and Florian Luca, Positive integers divisible by the product of their nonzero digits, Port. Math. 64 (2007) 75-85. (This proof for upper bounds contains an error. See the paper below)
Jean-Marie De Koninck and Florian Luca, Corrigendum to "Positive integers divisible by the product of their nonzero digits", Portugaliae Math. 64 (2007), 1: 75-85, Port. Math. 74 (2017), 169-170.
Qizheng He and Carlo Sanna, Counting numbers that are divisible by the product of their digits, arXiv:2403.14812 [math.NT], 2024.
Giovanni Resta, Zuckerman numbers, Numbers Aplenty.
Index entries for Colombian or self numbers and related sequences

Cf. A034709, A001103, A005349, A288069.
Cf. A286590 (for factorial-base analog).
Subsequence of A002796, A034838, and A055471.

import Data.List (elemIndices)
a007602 n = a007602_list !! (n-1)
a007602_list = map succ $ elemIndices 1 $ map a188642 [1..]
-- Reinhard Zumkeller, Apr 07 2011

[ n: n in [1..2144] | not IsZero(&*Intseq(n)) and IsZero(n mod &*Intseq(n)) ];  // Bruno Berselli, May 28 2011

filter:= proc(n)
local p;
p:= convert(convert(n,base,10),`*`);
p <> 0 and n mod p = 0
end proc;
select(filter, [$1..10000]); # Robert Israel, Aug 24 2014

zuckerQ[n_] := Module[{d = IntegerDigits[n], prod}, prod = Times @@ d; prod > 0 && Mod[n, prod] == 0]; Select[Range[5000], zuckerQ] (* Alonso del Arte, Aug 04 2004 *)

for(n=1,10^5,d=digits(n);p=prod(i=1,#d,d[i]);if(p&&n%p==0,print1(n,", "))) \\ Derek Orr, Aug 25 2014

from operator import mul
from functools import reduce
A007602 = [n for n in range(1,10**5) if not (str(n).count('0') or n % reduce(mul, (int(d) for d in str(n))))] # Chai Wah Wu, Aug 25 2014

A034709 Numbers divisible by their last digit.

Original entry on oeis.org

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, 111, 112, 115, 121, 122, 123, 124, 125, 126, 128, 131, 132

Offset: 1

Erich Friedman

Union of A017281, A017293, A139222, A139245, A017329, A139249, A139264, A139279 and A139280. - Reinhard Zumkeller, Jun 22 2008
The differences between consecutive terms repeat with period 1177 and the corresponding terms differ by 2520 = LCM(1,2,...,9). In other words, a(k*1177+i) = 2520*k + a(i). - Giovanni Resta, Aug 20 2015
The asymptotic density of this sequence is 1177/2520 = 0.467063... (see A341431 and A341432 for the values in other base representations). - Amiram Eldar, Nov 24 2022

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A010879, A034838, A007602.
Cf. A017281, A017293, A139222, A139245, A017329, A139249, A139264, A139279, A139280.
Cf. A341431, A341432.

import Data.Char (digitToInt)
a034709 n = a034709_list !! (n-1)
a034709_list =
   filter (\i -> i `mod` 10 > 0 && i `mod` (i `mod` 10) == 0) [1..]
-- Reinhard Zumkeller, Jun 19 2011

N:= 1000: # to get all terms <= N
sort([seq(seq(ilcm(10,d)*x+d, x=0..floor((N-d)/ilcm(10,d))), d=1..9)]); # Robert Israel, Aug 20 2015

dldQ[n_]:=Module[{idn=IntegerDigits[n],last1},last1=Last[idn]; last1!= 0&&Divisible[n,last1]]; Select[Range[150],dldQ]  (* Harvey P. Dale, Apr 25 2011 *)
Select[Range[150],Mod[#,10]!=0&&Divisible[#,Mod[#,10]]&] (* Harvey P. Dale, Aug 07 2022 *)

for(n=1,200,if(n%10,if(!(n%digits(n)[#Str(n)]),print1(n,", ")))) \\ Derek Orr, Sep 19 2014

A034709_list = [n for n in range(1, 1000) if n % 10 and not n % (n % 10)]
# Chai Wah Wu, Sep 18 2014

A002796 Numbers that are divisible by each nonzero digit.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, 22, 24, 30, 33, 36, 40, 44, 48, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 101, 102, 104, 105, 110, 111, 112, 115, 120, 122, 124, 126, 128, 132, 135, 140, 144, 150, 155, 162, 168, 175, 184, 200, 202, 204, 208, 210, 212

Offset: 1

N. J. A. Sloane

If n is a member so is 10*n. Also all repunits are members. - Robert G. Wilson v, Apr 12 2015
The repdigits are also members because they're always the repunit number of the same length multiplied by the digit being repeated. - Eric Fox, Sep 02 2019
The number of terms < 10^k: 9, 32, 137, 751, 4577, 29950, 207197, 1495637, ... . - Robert G. Wilson v, Apr 13 2015
Includes all multiples of 2520. - Robert Israel, Apr 15 2015
For n >= 10: A067458(a(n)) = 0. - Reinhard Zumkeller, Sep 24 2015

Lindon, Visible factor numbers, J. Rec. Math., 1 (1968), 217.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 1..2000
Index entries for 10-automatic sequences.

Cf. A007602, A034838, A237851.
Cf. A171492 (complement).
Cf. A067458.

import Data.List (nub, sort); import Data.Char (digitToInt)
a002796 n = a002796_list !! (n-1)
a002796_list = filter f [1..] where
   f x = all ((== 0) . mod x) ds where
     ds = map digitToInt (if c == '0' then cs else cs')
     cs'@(c:cs) = nub $ sort $ show x
-- Reinhard Zumkeller, Jan 01 2014

sol:=[];for k in [1..220] do a:=Set(Intseq(k)) diff {0}; if #[c:c in a|IsIntegral(k/c)] eq #a then; Append(~sol,k); end if; end for; sol; // Marius A. Burtea, Sep 09 2019

select(t -> t mod ilcm(op(convert(convert(t,base,10),set) minus {0})) = 0, [$1..1000]); # Robert Israel, Apr 15 2015

dQ[n_]:=Module[{nzidn=DeleteCases[IntegerDigits[n],0]},And@@Divisible[n, nzidn]]; Select[Range[250],dQ] (* Harvey P. Dale, Dec 13 2011 *)

is(n)=my(v=vecsort(eval(Vec(Str(n))),,8));for(i=1+(v[1]==0), #v, if(n%v[i],return(0)));1 \\ Charles R Greathouse IV, Apr 17 2012

A002796_list = []
for i in range(1,10**5):
    for d in set(str(i)):
        if d != '0' and i % int(d):
            break
    else:
        A002796_list.append(i) # Chai Wah Wu, Mar 26 2021

a(n) ~ 2520*n. - Charles R Greathouse IV, Feb 13 2017

More terms from Henry Bottomley, Jun 06 2000

A115569 Lynch-Bell numbers: numbers n such that the digits are all different (and do not include 0) and n is divisible by each of its individual digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 24, 36, 48, 124, 126, 128, 132, 135, 162, 168, 175, 184, 216, 248, 264, 312, 315, 324, 384, 396, 412, 432, 612, 624, 648, 672, 728, 735, 784, 816, 824, 864, 936, 1236, 1248, 1296, 1326, 1362, 1368, 1395, 1632, 1692, 1764, 1824

Offset: 1

Mike Smith (mtm_king(AT)yahoo.com), Mar 10 2006; also submitted by Andy Edwards (AndynGen(AT)aol.com), Mar 20 2006

This is a subset of some of the related sequences listed below. Stephen Lynch and Andrew Bell are Brisbane surgeons who contributed to the identification of this sequence.
There are 548 Lynch-Bell numbers. A117911 gives the number of n-digit ones. The digit 5 cannot appear in Lynch-Bell numbers containing an even digit; 5 must be the units digit when it appears. The 7-digit Lynch-Bell numbers are 105 permutations of 1289736 (the smallest such). - Rick L. Shepherd, Apr 01 2006
Can be seen/read as a table with row lengths A117911 (rows r > 7 have zero length). - M. F. Hasler, Jan 31 2016

			384/3 = 128, 384/8 = 48, 384/4 = 96. Thus 384 is Lynch-Bell as it is a multiple of each of its three distinct digits.

Rick L. Shepherd, List of all terms

Cf. A034838, A034709, A063527.

Cf. A117911, A117912 (have even digits only), A117913 (have odd digits only), A010784.

with(combinat):
f:= l-> parse(cat(l[])):
T:= n-> sort(map(f, select(l-> andmap(x-> irem(f(l), x)=0, l),
         map(p-> permute(p)[], choose([$1..9], n)))))[]:
seq(T(n), n=1..7);  # Alois P. Heinz, Jul 31 2022

Reap[For[n = 1, n < 10^7, n++, id = IntegerDigits[n]; If[FreeQ[id, 0] && Length[id] == Length[Union[id]] && And @@ (Divisible[n, #]& /@ id), Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Nov 26 2013 *)
bnQ[n_]:=Max[DigitCount[n]]==1&&FreeQ[IntegerDigits[n],0]&&Union[Divisible[n,IntegerDigits[ n]]]=={True}; Select[Range[2000],lbnQ] (* Harvey P. Dale, Jun 02 2023 *)
Cases[Union @@ ((FromDigits@#&/@Flatten[Permutations@# & /@ Subsets[Range@9, {#}], 1])&/@ Range@9), ?(DeleteDuplicates[Divisible[#, IntegerDigits@#]] == {True} &)] (* _Hans Rudolf Widmer, Aug 27 2024 *)

A115569_row(n)={if(n,my(u=vectorv(n,i,10^i)\10,S=List(),M);forvec(v=vector(n,i,[1,9]),(M=lcm(v))%10==0||normlp(v,1)%3^valuation(M,3)||for(k=1,n!,vecextract(v,numtoperm(n,k))*u%M ||listput(S,vecextract(v,numtoperm(n,k))*u)),2);Set(S),concat(apply(A115569_row,[1..7])))} \\ Return terms of length n if given, else the vector of all terms. The checks M%10 and |v| % 3^v(...) are not needed but reduce CPU time by 97%. - M. F. Hasler, Jan 31 2016

A115569(n)=n>9&&for(r=2,7,(n-=#t=A115569_row(r))>9||return(t[n-9+#t]));n \\ M. F. Hasler, Jan 31 2016

def ok(n):
    s = str(n)
    if "0" in s or len(set(s)) < len(s): return False
    return all(n%int(d) == 0 for d in s)
afull = [k for k in range(9867313) if ok(k)]
print(afull[:55]) # Michael S. Branicky, Jul 31 2022

The full list of terms was sent in by Rick L. Shepherd (see link) and also by Sébastien Dumortier, Apr 04 2006

A132359 Numbers divisible by the square of their last decimal digit.

Original entry on oeis.org

1, 11, 12, 21, 25, 31, 32, 36, 41, 51, 52, 61, 63, 64, 71, 72, 75, 81, 91, 92, 101, 111, 112, 121, 125, 128, 131, 132, 141, 144, 147, 151, 152, 153, 161, 171, 172, 175, 181, 191, 192, 201, 211, 212, 216, 221, 224, 225, 231, 232, 241, 243, 251, 252, 261, 271, 272

Offset: 1

Jonathan Vos Post, Nov 08 2007

Subsequences are A017281 and A053742 representing last digits 1 and 5. Generators for the subsequences representing last digits 2, 3, 4, 6, 7, 8 and 9 are, in that order, the terms 12+20i, 63+90i, 64+80i, 36+180i, 147+490i, 128+320i, 729+810i, where i=0,1,2,... - R. J. Mathar, Nov 13 2007

This is a 10-automatic sequence. - Charles R Greathouse IV, Dec 28 2011

			147 belongs to the sequence because 147/7^2 = 3.

T. D. Noe and Christian N. K. Anderson, Table of n, a(n) for n = 1..10000 (first 1000 values from T. D. Noe)
Index entries for 10-automatic sequences.

Cf. A034709, A225722, A221651, A225296, A225297, A034709, A034837, A005349, A007602, A034838, A225297.

isA132359 := proc(n) local ldig ; ldig := n mod 10 ; if ldig <> 0 and n mod (ldig^2) = 0 then true ; else false ; fi ; end: for n from 1 to 400 do if isA132359(n) then printf("%d,",n) ; fi ; od: # R. J. Mathar, Nov 13 2007
a:=proc(n) local nn: nn:=convert(n,base,10): if 0 < nn[1] and `mod`(n,nn[1]^2) =0 then n else end if end proc: seq(a(n),n=1..250); # Emeric Deutsch, Nov 15 2007

Select[Range[250], IntegerDigits[ # ][[ -1]] > 0 && Mod[ #, IntegerDigits[ # ][[ -1]]^2] == 0 &] (* Stefan Steinerberger, Nov 12 2007 *)
dsldQ[n_]:=Module[{lidnsq=Last[IntegerDigits[n]]^2},lidnsq!=0 && Divisible[n,lidnsq]]; Select[Range[300],dsldQ] (* Harvey P. Dale, May 03 2011 *)

is(n)=n%(n%10)^2==0 \\ Charles R Greathouse IV, Dec 28 2011

def ok(n): return n%10 > 0 and n%(n%10)**2 == 0
print([k for k in range(273) if ok(k)]) # Michael S. Branicky, Jul 03 2022

which(sapply(1:500,function(x) isint(x/(x%%10)^2))) # Christian N. K. Anderson, May 04 2013

Numbers k such that fp[k / (k mod 10)] = 0.

a(n) ~ 6350400*n/1241929 = 5.113...*n. - Charles R Greathouse IV, Dec 28 2011

Corrected and extended by Stefan Steinerberger, Emeric Deutsch and R. J. Mathar, Nov 12 2007

A063527 Numbers that are divisible by all of their 1 and 2 digit substrings.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99, 1111, 1155, 1248, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 27216, 31248, 111111, 116688, 121212, 142128, 212184, 222222, 242424, 313131, 321216, 333333, 363636, 368424, 444444

Offset: 1

Erich Friedman, Aug 01 2001

Subsequence of A034838. - Michel Marcus, Sep 19 2014

			1155 is divisible by 1, 1, 5, 5, 11, 15 and 55.

David A. Corneth, Table of n, a(n) for n = 1..10442
Index entries for 10-automatic sequences.

Cf. A034838 (integers divisible by all their digits).

d12Q[n_]:=Module[{idn=IntegerDigits[n],idn2},idn2=FromDigits/@Partition[ idn,2,1];FreeQ[idn,0]&&And@@Divisible[n,idn]&&And@@Divisible[n,idn2]]; Select[Range[400000],d12Q] (* Harvey P. Dale, Aug 11 2015 *)

is(n) = {my(d = digits(n), t = 0); s = Set(d); if(s[1] == 0, return(0)); for(i = 1, 2, for(j = 1, #d - i + 1, t++; fr = fromdigits(vector(i, k, d[j+k-1])); if(n % fr != 0, return(0)); ) ); 1 } \\ David A. Corneth, Sep 17 2019

from itertools import product
A063527_list = []
for g in range(1,7):
    for n in product('123456789', repeat=g):
        s = ''.join(n)
        m = int(s)
        if not any([m % int(d) for d in s]):
            for i in range(len(s)-1):
                if m % int(s[i:i+2]):
                    break
            else:
                A063527_list.append(m) # Chai Wah Wu, Sep 18 2014

More terms from David A. Corneth, Sep 17 2019

A066484 Numbers with at least 2 distinct digits and whose "rotations" (including the number itself) are multiples of these digits; repeated digits allowed but digit 0 not allowed.

Original entry on oeis.org

1113, 1131, 1311, 2226, 2262, 2622, 3111, 3339, 3393, 3933, 6222, 9333, 11133, 11313, 11331, 13113, 13131, 13311, 22266, 22626, 22662, 26226, 26262, 26622, 31113, 31131, 31311, 33111, 33399, 33939, 33993, 39339, 39393, 39933, 62226, 62262, 62622, 66222, 93339, 93393, 93933, 99333, 111333, 111339, 111393

Offset: 1

Sudipta Das (juitech(AT)vsnl.net), Jan 02 2002

"Rotation" of a (multi-digit) number involves taking the first digit of the number and putting it at the end to form a new number. For example, successive rotations of 1234 yield the numbers 2341, 3412 and 4123 (another rotation gives back the original number).

Subsequence of A034838, A052382 and of A139819. - Reinhard Zumkeller, Nov 29 2012

			The rotations of 137179 are 371791, 717913, 179137, 791371, 913717, 137179; all these are divisible by 1, 3, 7 and 9.

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Ken Duisenberg, Puzzle of the Week (Dec 14, 2001), Dividing Rotated Numbers

-- import Data.List (nub, inits, tails)
a066484 n = a066484_list !! (n-1)
a066484_list = filter h [1..] where
   h x = notElem '0' xs && length (nub xs) > 1 &&
         all d (map read $ zipWith (++)
               (tail $ tails xs) (tail $ inits xs)) where xs = show x
   d u = g u where
         g v = v == 0 || mod u d == 0 && g v' where (v', d) = divMod v 10
-- Reinhard Zumkeller, Nov 29 2012

ddQ[n_]:=Module[{idn=IntegerDigits[n]},DigitCount[n,10,0]==0 && Length[Union[idn]]>1 && And@@Flatten[Divisible[#,Union[idn]]&/@ (FromDigits/@Table[RotateRight[idn,i], {i,Length[idn]}])]]; Select[Range[10,200000],ddQ]  (* Harvey P. Dale, Mar 30 2011 *)

select( {is_A066484(n,d=Set(digits(n)))= d[1] && #d>1 && (d[1]>1||d=d[^1]) && !for(i=0,logint(n,10),n=[1,10^logint(n,10)]*divrem(n,10);[n%x|x<-d]&&return)}, [1..10^5]) \\ M. F. Hasler, Jan 05 2020

Corrected and extended by Harvey P. Dale, Mar 30 2011

Definition reworded by M. F. Hasler, Jan 05 2020

A051004 Numbers divisible both by their individual digits and by the sum of their digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 48, 111, 112, 126, 132, 135, 144, 162, 216, 222, 224, 264, 288, 312, 315, 324, 333, 336, 396, 432, 444, 448, 555, 612, 624, 648, 666, 735, 777, 864, 888, 936, 999, 1116, 1122, 1128, 1164, 1212, 1224, 1236, 1296, 1332

Offset: 1

Eric W. Weisstein

No zero digits permitted. [Harvey P. Dale, Dec 18 2011]

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Digit

Intersection of A005349 and A034838.

Cf. A038369, A087142.

a051004 n = a051004_list !! (n-1)
a051004_list =  [x | x <- a005349_list,
                     x == head (dropWhile (< x) a034838_list)]
-- Reinhard Zumkeller, Mar 03 2012

ddQ[n_]:=Module[{idn=IntegerDigits[n]},!MemberQ[idn,0] && Divisible[ n,Total[idn]]&& And @@ Divisible[n,idn]]; Select[Range[1400],ddQ] (* Harvey P. Dale, Dec 18 2011 *)

Offset corrected by Reinhard Zumkeller, Mar 03 2012

A087142 Numbers divisible by their individual digits, but not by the sum of their digits (counted with multiplicity).

Original entry on oeis.org

11, 15, 22, 33, 44, 55, 66, 77, 88, 99, 115, 122, 124, 128, 155, 168, 175, 184, 212, 244, 248, 366, 384, 412, 424, 488, 515, 636, 672, 728, 784, 816, 824, 848, 1111, 1112, 1113, 1115, 1124, 1131, 1144, 1155, 1176, 1184, 1197, 1222, 1244, 1248, 1266, 1288, 1311

Offset: 1

Reinhard Zumkeller, Aug 18 2003

Intersection of A034838 and A065877.

			488 is in the sequence as its divisible by its individual digits but not by the sum of its digits counted with multiplicity. That is 488 is divisible by 4 and 8 but not by 4 + 8 + 8 = 20. - _David A. Corneth_, Jan 28 2021

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Cf. A034838, A052382, A065877, A087141.

Cf. A337163 (similar, with product).

didQ[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,0]&&AllTrue[n/idn, IntegerQ] && !Divisible[n,Total[idn]]]; Select[Range[1300], didQ] (* The program uses the AllTrue function from Mathematica version 10 *)  (* Harvey P. Dale, Apr 18 2016 *)

is(n) = { my(d = digits(n), sd = vecsum(d), s = Set(d)); if(n == 0 || s[1] == 0, return(0)); if(n % sd != 0, for(i = 1, #s, if(n % s[i] != 0, return(0) ) ); return(1) ); 0 } \\ David A. Corneth, Jan 28 2021

def ok(n):
    d = list(map(int, str(n)))
    return 0 not in d and n%sum(d) and all(n%di == 0 for di in set(d))
print([k for k in range(1312) if ok(k)]) # Michael S. Branicky, Nov 15 2021

A221651 Numbers divisible by their first digit squared (excluding those whose first digit is 1).

Original entry on oeis.org

20, 24, 28, 36, 48, 50, 200, 204, 208, 212, 216, 220, 224, 228, 232, 236, 240, 244, 248, 252, 256, 260, 264, 268, 272, 276, 280, 284, 288, 292, 296, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 400, 416, 432, 448, 464, 480, 496, 500, 525, 550, 575

Offset: 1

Kevin L. Schwartz and Christian N. K. Anderson, May 04 2013

Numbers where floor(n/10^floor(log(n)))^2 divides n.

			48 is divisible by 4^2.

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
Christian N. K. Anderson, Ulam Spiral for the first 10000 terms. [Draw the usual Ulam spiral, containing all the nonnegative integers, and color the numbers belonging to this sequence yellow]

Cf. A132359, A034709, A034837, A005349, A007602, A034838, A225297, A225722, A225683.

x=0; y=rep(0,1000); len=0
firstdig<-function(x) as.numeric(substr(as.character(x),1,1))
isint<-function(x) x==as.integer(x)
while(len<10000) if((fd=firstdig((x=x+1)))>1) if(isint(x/fd^2)) y[(len=len+1)]=x

cp's OEIS Frontend

A007602 Numbers that are divisible by the product of their digits.

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A034709 Numbers divisible by their last digit.

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A002796 Numbers that are divisible by each nonzero digit.

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A115569 Lynch-Bell numbers: numbers n such that the digits are all different (and do not include 0) and n is divisible by each of its individual digits.

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A132359 Numbers divisible by the square of their last decimal digit.

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A063527 Numbers that are divisible by all of their 1 and 2 digit substrings.

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