login
Numbers whose sum of reciprocals of digits is the reciprocal of an integer.
6

%I #32 Sep 29 2024 11:46:10

%S 1,2,3,4,5,6,7,8,9,22,36,44,63,66,88,236,244,263,326,333,362,424,442,

%T 488,623,632,666,848,884,999,2488,2666,2848,2884,3366,3446,3464,3636,

%U 3644,3663,4288,4346,4364,4436,4444,4463,4634,4643,4828,4882,6266,6336

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

%C Intersection of A214958 and A052382: A214949(a(n))*A168046(a(n)) = 1. - _Reinhard Zumkeller_, Aug 02 2012

%H T. D. Noe, <a href="/A037264/b037264.txt">Table of n, a(n) for n = 1..1232</a> (complete sequence)

%e 63 is a term: 1/((1/6) + (1/3)) = 2.

%t 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 Select[Range[6500],FreeQ[IntegerDigits[#],0]&&IntegerQ[1/Total[1/IntegerDigits[#]]]&] (* _Harvey P. Dale_, Sep 29 2024 *)

%o (Haskell)

%o a037264 n = a037264_list !! (n-1)

%o a037264_list = filter ((== 1) . a168046) $

%o takeWhile (<= 999999999) a214958_list

%o -- _Reinhard Zumkeller_, Aug 02 2012

%o (PARI) isok(n) = {my(d=digits(n)); vecmin(d) && (numerator(sum(k=1, #d, 1/d[k])) == 1);} \\ _Michel Marcus_, May 24 2018

%o (Python)

%o from fractions import Fraction

%o def ok(n):

%o ds = list(map(int, str(n)))

%o return 0 not in ds and sum(Fraction(1, d) for d in ds).numerator == 1

%o print(list(filter(ok, range(1, 6337)))) # _Michael S. Branicky_, Aug 08 2021

%Y Cf. A037265, A045910.

%K easy,nonn,nice,base,fini,full

%O 1,2

%A _Naohiro Nomoto_