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

1,2

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

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 *)

Prog

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

Crossrefs

Cf. A052382, A168046, A214950, A214957.

Sequence in context: A047902 A081930 A143964 * A091784 A213972 A061852

Adjacent sequences: A034705 A034706 A034707 * A034709 A034710 A034711

Keyword

nonn,base,nice

Author

Erich Friedman

Status

approved