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A037264 Numbers whose sum of reciprocals of digits is the reciprocal of an integer.

%I A037264 #32 Sep 29 2024 11:46:10
%S A037264 1,2,3,4,5,6,7,8,9,22,36,44,63,66,88,236,244,263,326,333,362,424,442,
%T A037264 488,623,632,666,848,884,999,2488,2666,2848,2884,3366,3446,3464,3636,
%U A037264 3644,3663,4288,4346,4364,4436,4444,4463,4634,4643,4828,4882,6266,6336
%N A037264 Numbers whose sum of reciprocals of digits is the reciprocal of an integer.
%C A037264 Intersection of A214958 and A052382: A214949(a(n))*A168046(a(n)) = 1. - _Reinhard Zumkeller_, Aug 02 2012
%H A037264 T. D. Noe, <a href="/A037264/b037264.txt">Table of n, a(n) for n = 1..1232</a> (complete sequence)
%e A037264 63 is a term: 1/((1/6) + (1/3)) = 2.
%t A037264 Reap[Do[If[FreeQ[id = IntegerDigits[n], 0], If[IntegerQ[1/Total[1/id]], Sow[n]]], {n, 1, 10^4}]][[2, 1]] (* _Jean-François Alcover_, Dec 15 2015 *)
%t A037264 Select[Range[6500],FreeQ[IntegerDigits[#],0]&&IntegerQ[1/Total[1/IntegerDigits[#]]]&] (* _Harvey P. Dale_, Sep 29 2024 *)
%o A037264 (Haskell)
%o A037264 a037264 n = a037264_list !! (n-1)
%o A037264 a037264_list = filter ((== 1) . a168046) $
%o A037264                       takeWhile (<= 999999999) a214958_list
%o A037264 -- _Reinhard Zumkeller_, Aug 02 2012
%o A037264 (PARI) isok(n) = {my(d=digits(n)); vecmin(d) && (numerator(sum(k=1, #d, 1/d[k])) == 1);} \\ _Michel Marcus_, May 24 2018
%o A037264 (Python)
%o A037264 from fractions import Fraction
%o A037264 def ok(n):
%o A037264     ds = list(map(int, str(n)))
%o A037264     return 0 not in ds and sum(Fraction(1, d) for d in ds).numerator == 1
%o A037264 print(list(filter(ok, range(1, 6337)))) # _Michael S. Branicky_, Aug 08 2021
%Y A037264 Cf. A037265, A045910.
%K A037264 easy,nonn,nice,base,fini,full
%O A037264 1,2
%A A037264 _Naohiro Nomoto_