This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A221644 #25 May 16 2018 09:45:15
%S A221644 1,11,12,24,33,111,113,121,123,139,142,146,155,184,212,216,222,226,
%T A221644 241,243,331,333,369,414,424,482,486,649,662,666,848,1111,1112,1114,
%U A221644 1128,1131,1132,1134,1168,1177,1196,1211,1212,1214,1228,1231,1232,1234,1268
%N A221644 Let abcd... be the decimal expansion of k. Sequence lists numbers k such that 1/a + 2/b + 3/c + 4/d + ... is an integer.
%C A221644 The repunits numbers 1, 11, 111, 1111, ... (A002275) are in the sequence.
%C A221644 The first nine terms 1, 12, 123, 1234, ... of A007908 are in the sequence.
%C A221644 If a number of the form ab1 is in the sequence, the corresponding number of the form ab3 is also in the sequence.
%C A221644 If a number of the form abc1 is in the sequence, the corresponding number of the form abc2 is also in the sequence.
%C A221644 If a number of the form abc11 is in the sequence, the corresponding number of the form abc15 is also in the sequence.
%C A221644 The first nine terms 1, 12, 113, 1114, 11115, ... of A198375 are in the sequence.
%C A221644 In the general case, if n = abcd...q is in the sequence where q is the k-th decimal digit of n, the number abcd...qr is also in the sequence if k+1 is divisible by r; for example, 82812 is in the sequence => 828121, 828122, 828123 and 828126 are also in the sequence because 6 is divisible by 1, 2, 3 and 6.
%H A221644 Michel Lagneau, <a href="/A221644/b221644.txt">Table of n, a(n) for n = 1..10000</a>
%e A221644 184 is in the sequence because 1/1 + 2/8 + 3/4 = 2.
%p A221644 with(numtheory):for n from 1 to 2000 do: d:=convert(n, base, 10):n1:=nops(d):p:=product('d[i]', 'i'=1..n1):if p<>0 then s:=sum('i/d[n1-i+1] ', 'i'=1..n1):if s=floor(s) then printf(`%d, `,n):else fi:fi:od:
%t A221644 Select[Range[1300],FreeQ[IntegerDigits[#],0]&&IntegerQ[Total[ Range[ IntegerLength[ #]]/ IntegerDigits[ #]]]&] (* _Harvey P. Dale_, May 16 2018 *)
%o A221644 (PARI) isok(n) = my(d=digits(n)); vecmin(d) && (denominator(sum(k=1, #d, k/d[k])) == 1); \\ _Michel Marcus_, Sep 14 2017
%Y A221644 Cf. A002275, A007908, A198375.
%K A221644 nonn,base,less
%O A221644 1,2
%A A221644 _Michel Lagneau_, Aug 08 2013