Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #26 Feb 17 2024 10:28:36
%S 1,11,22,111,122,212,221,236,244,263,326,333,362,424,442,623,632,1111,
%T 1122,1212,1221,1236,1244,1263,1326,1333,1362,1424,1442,1623,1632,
%U 2112,2121,2136,2144,2163,2211,2222,2316,2361,2414,2441,2488,2613,2631,2666
%N Numbers for which the sum of reciprocals of digits is an integer.
%C Intersection of A214957 and A052382: A214950(a(n))*A168046(a(n)) = 1. - _Reinhard Zumkeller_, Aug 02 2012
%H Reinhard Zumkeller, <a href="/A034708/b034708.txt">Table of n, a(n) for n = 1..1000</a>
%t 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 Select[Range[3000],DigitCount[#,10,0]==0 && IntegerQ[Total[ 1/IntegerDigits[#]]]&] (* _Harvey P. Dale_, May 06 2012 *)
%o (Haskell)
%o a034708 n = a034708_list !! (n-1)
%o a034708_list = filter ((== 1) . a168046) a214957_list
%o -- _Reinhard Zumkeller_, Aug 02 2012
%o (PARI) isok(n) = {my(d = digits(n)); vecmin(d) && denominator(sum(k=1, #d, 1/d[k])) == 1;} \\ _Michel Marcus_, Feb 12 2016
%o (Python)
%o from fractions import Fraction
%o def srd(n): return sum(Fraction(1, int(d)) for d in str(n)) # assumes no 0's
%o def ok(n): return False if '0' in str(n) else srd(n).denominator == 1
%o def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
%o print(aupto(2666)) # _Michael S. Branicky_, Jan 11 2021
%Y Cf. A052382, A168046, A214950, A214957.
%K nonn,base,nice
%O 1,2
%A _Erich Friedman_