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A214949 Numerator of sum of reciprocals of all nonzero digits of n in decimal representation.

%I A214949 #13 Jan 26 2022 17:58:30
%S A214949 0,1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,10,1,3,1,5,3,7,2,9,5,11,1,4,5,
%T A214949 2,7,8,1,10,11,4,1,5,3,7,1,9,5,11,3,13,1,6,7,8,9,2,11,12,13,14,1,7,2,
%U A214949 1,5,11,1,13,7,5,1,8,9,10,11,12,13,2,15,16
%N A214949 Numerator of sum of reciprocals of all nonzero digits of n in decimal representation.
%H A214949 Reinhard Zumkeller, <a href="/A214949/b214949.txt">Table of n, a(n) for n = 0..10000</a>
%F A214949 a(A037264(n)) = a(A037268(n)) = a(A214958(n)) = a(A214959(n)) = 1;
%F A214949 a(n) = a(A004719(n)).
%t A214949 nsr[n_] := Numerator[Total[1/Select[IntegerDigits[n], # > 0 &]]]; nsr /@ Range[0, 79] (* _Jayanta Basu_, Jul 13 2013 *)
%o A214949 (Haskell)
%o A214949 import Data.Ratio ((%), numerator)
%o A214949 a214949 = f 0 where
%o A214949    f y 0 = numerator y
%o A214949    f y x = f (y + if d == 0 then 0 else 1 % d) x'
%o A214949            where (x',d) = divMod x 10
%o A214949 (PARI) a(n) = my(d=digits(n)); numerator(sum(k=1, #d, if (d[k], 1/d[k]))); \\ _Michel Marcus_, Jan 26 2022
%Y A214949 Cf. A004719, A037264, A037268, A214958, A214959.
%Y A214949 Cf. A214950 (denominators).
%K A214949 nonn,base,frac
%O A214949 0,12
%A A214949 _Reinhard Zumkeller_, Aug 02 2012