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A034708 Numbers for which the sum of reciprocals of digits is an integer.

%I A034708 #26 Feb 17 2024 10:28:36
%S A034708 1,11,22,111,122,212,221,236,244,263,326,333,362,424,442,623,632,1111,
%T A034708 1122,1212,1221,1236,1244,1263,1326,1333,1362,1424,1442,1623,1632,
%U A034708 2112,2121,2136,2144,2163,2211,2222,2316,2361,2414,2441,2488,2613,2631,2666
%N A034708 Numbers for which the sum of reciprocals of digits is an integer.
%C A034708 Intersection of A214957 and A052382: A214950(a(n))*A168046(a(n)) = 1. - _Reinhard Zumkeller_, Aug 02 2012
%H A034708 Reinhard Zumkeller, <a href="/A034708/b034708.txt">Table of n, a(n) for n = 1..1000</a>
%t A034708 f[ n_ ] := 1/n a[ n_ ] := Apply[ Plus, Map[ f, IntegerDigits[ n ] ] ] Select[ Range[ 1000 ], FreeQ[ IntegerDigits[ # ], 0 ] && IntegerQ[ a [ # ] ] & ] (* _Santi Spadaro_, Oct 13 2001 *)
%t A034708 Select[Range[3000],DigitCount[#,10,0]==0 && IntegerQ[Total[ 1/IntegerDigits[#]]]&] (* _Harvey P. Dale_, May 06 2012 *)
%o A034708 (Haskell)
%o A034708 a034708 n = a034708_list !! (n-1)
%o A034708 a034708_list = filter ((== 1) . a168046) a214957_list
%o A034708 -- _Reinhard Zumkeller_, Aug 02 2012
%o A034708 (PARI) isok(n) = {my(d = digits(n)); vecmin(d) && denominator(sum(k=1, #d, 1/d[k])) == 1;} \\ _Michel Marcus_, Feb 12 2016
%o A034708 (Python)
%o A034708 from fractions import Fraction
%o A034708 def srd(n): return sum(Fraction(1, int(d)) for d in str(n)) # assumes no 0's
%o A034708 def ok(n): return False if '0' in str(n) else srd(n).denominator == 1
%o A034708 def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
%o A034708 print(aupto(2666)) # _Michael S. Branicky_, Jan 11 2021
%Y A034708 Cf. A052382, A168046, A214950, A214957.
%K A034708 nonn,base,nice
%O A034708 1,2
%A A034708 _Erich Friedman_