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A291256 Numbers n such that Sum_{k>=1} digits(k)/k = 1 where digits() are the digits of n in base 10, the least significant digit having index 1.

%I A291256 #11 Aug 22 2017 03:22:57
%S A291256 1,20,300,2010,4000,50000,100110,102100,200200,300010,302000,400100,
%T A291256 600000,7000000,20001010,20003000,20101100,20301000,40000010,40002000,
%U A291256 40100100,40300000,60001000,80000000,300000200,300100010,300102000,300200100,300400000,320101000,340100000
%N A291256 Numbers n such that Sum_{k>=1} digits(k)/k = 1 where digits() are the digits of n in base 10, the least significant digit having index 1.
%H A291256 Michel Marcus and Giovanni Resta, <a href="/A291256/b291256.txt">Table of n, a(n) for n = 1..10000</a> (first 59 terms from Michel Marcus)
%e A291256 20 is a term since 0/1 + 2/2 = 1.
%e A291256 2010 is a term since 0/1 + 1/2 + 0/3 + 2/4 = 1.
%t A291256 ndig[n_] := Sort[Sum[e[[2]] 10^(1/e[[1]] - 1), {e, #}] & /@ Select[Tally /@ (Join[ {1/n}, #] & /@ IntegerPartitions[1 - 1/n, All, 1/Range[n]]), Max[Flatten[#]] < 10 &]]; Join @@ (ndig /@ Range[20]) (* _Giovanni Resta_, Aug 21 2017 *)
%o A291256 (PARI) isok(n) = my(d = Vecrev(digits(n))); sum(k=1, #d, d[k]/k) == 1;
%Y A291256 Cf. A272036 (analog in base 2).
%K A291256 nonn,base
%O A291256 1,2
%A A291256 _Michel Marcus_, Aug 21 2017