A037264 Numbers whose sum of reciprocals of digits is the reciprocal of an integer.

1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 36, 44, 63, 66, 88, 236, 244, 263, 326, 333, 362, 424, 442, 488, 623, 632, 666, 848, 884, 999, 2488, 2666, 2848, 2884, 3366, 3446, 3464, 3636, 3644, 3663, 4288, 4346, 4364, 4436, 4444, 4463, 4634, 4643, 4828, 4882, 6266, 6336

Offset: 1

Author

Naohiro Nomoto

Keywords

• easy
• nonn
• nice
• base
• fini
• full

Comments

Intersection of A214958 and A052382: A214949(a(n))*A168046(a(n)) = 1. - Reinhard Zumkeller, Aug 02 2012

Examples

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..1232 (complete sequence)

Crossrefs

Cf. A037265, A045910.

Programs

Haskell

a037264 n = a037264_list !! (n-1)
a037264_list = filter ((== 1) . a168046) $
                      takeWhile (<= 999999999) a214958_list
-- Reinhard Zumkeller, Aug 02 2012

Mathematica

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 *)
Select[Range[6500],FreeQ[IntegerDigits[#],0]&&IntegerQ[1/Total[1/IntegerDigits[#]]]&] (* Harvey P. Dale, Sep 29 2024 *)

PARI

isok(n) = {my(d=digits(n)); vecmin(d) && (numerator(sum(k=1, #d, 1/d[k])) == 1);} \\ Michel Marcus, May 24 2018

Python

from fractions import Fraction
def ok(n):
    ds = list(map(int, str(n)))
    return 0 not in ds and sum(Fraction(1, d) for d in ds).numerator == 1
print(list(filter(ok, range(1, 6337)))) # Michael S. Branicky, Aug 08 2021