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

1, 11, 22, 111, 122, 212, 221, 236, 244, 263, 326, 333, 362, 424, 442, 623, 632, 1111, 1122, 1212, 1221, 1236, 1244, 1263, 1326, 1333, 1362, 1424, 1442, 1623, 1632, 2112, 2121, 2136, 2144, 2163, 2211, 2222, 2316, 2361, 2414, 2441, 2488, 2613, 2631, 2666

Offset: 1

Author

Erich Friedman

Keywords

• nonn
• base
• nice

Comments

Intersection of A214957 and A052382: A214950(a(n))*A168046(a(n)) = 1. - Reinhard Zumkeller, Aug 02 2012

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A052382, A168046, A214950, A214957.

Programs

Haskell

a034708 n = a034708_list !! (n-1)
a034708_list = filter ((== 1) . a168046) a214957_list
-- Reinhard Zumkeller, Aug 02 2012

Mathematica

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 *)
Select[Range[3000],DigitCount[#,10,0]==0 && IntegerQ[Total[ 1/IntegerDigits[#]]]&] (* Harvey P. Dale, May 06 2012 *)

PARI

isok(n) = {my(d = digits(n)); vecmin(d) && denominator(sum(k=1, #d, 1/d[k])) == 1;} \\ Michel Marcus, Feb 12 2016

Python

from fractions import Fraction
def srd(n): return sum(Fraction(1, int(d)) for d in str(n)) # assumes no 0's
def ok(n): return False if '0' in str(n) else srd(n).denominator == 1
def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
print(aupto(2666)) # Michael S. Branicky, Jan 11 2021