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A214959 Numbers for which the sum of reciprocals of nonzero digits = 1.

%I A214959 #15 Sep 08 2022 08:46:02
%S A214959 1,10,22,100,202,220,236,244,263,326,333,362,424,442,623,632,1000,
%T A214959 2002,2020,2036,2044,2063,2200,2306,2360,2404,2440,2488,2603,2630,
%U A214959 2666,2848,2884,3026,3033,3062,3206,3260,3303,3330,3366,3446,3464,3602,3620,3636
%N A214959 Numbers for which the sum of reciprocals of nonzero digits = 1.
%C A214959 Intersection of A214957 and A214958: A214949(a(n))*A214950(a(n)) = 1.
%H A214959 Reinhard Zumkeller, <a href="/A214959/b214959.txt">Table of n, a(n) for n = 1..10000</a>
%t A214959 idnQ[n_]:=Total[1/Select[IntegerDigits[n],#>0&]]==1; Select[Range[ 4000],idnQ] (* _Harvey P. Dale_, Dec 08 2012 *)
%o A214959 (Haskell)
%o A214959 import Data.Ratio ((%), numerator, denominator)
%o A214959 a214959 n = a214959_list !! (n-1)
%o A214959 a214959_list = [x | x <- [0..], f x 0] where
%o A214959    f 0 v = numerator v == 1 && denominator v == 1
%o A214959    f u v | d > 0     = f u' (v + 1 % d)
%o A214959          | otherwise = f u' v  where (u',d) = divMod u 10
%o A214959 (Magma) SumReciprocalsDigits:=func<n | &+[1/d: d in Intseq(n) | not IsZero(d)]>; [n: n in [1..3636] | IsOne(SumReciprocalsDigits(n))]; // _Bruno Berselli_, Aug 02 2012
%Y A214959 Cf. A037268 (subsequence).
%K A214959 nonn,base
%O A214959 1,2
%A A214959 _Reinhard Zumkeller_, Aug 02 2012