A214958 -id:A214958 - cp's OEIS frontend

A214949 Numerator of sum of reciprocals of all nonzero digits of n in decimal representation.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 3, 1, 5, 3, 7, 2, 9, 5, 11, 1, 4, 5, 2, 7, 8, 1, 10, 11, 4, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 1, 6, 7, 8, 9, 2, 11, 12, 13, 14, 1, 7, 2, 1, 5, 11, 1, 13, 7, 5, 1, 8, 9, 10, 11, 12, 13, 2, 15, 16

Offset: 0

Reinhard Zumkeller, Aug 02 2012

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A004719, A037264, A037268, A214958, A214959.

Cf. A214950 (denominators).

import Data.Ratio ((%), numerator)
a214949 = f 0 where
   f y 0 = numerator y
   f y x = f (y + if d == 0 then 0 else 1 % d) x'
           where (x',d) = divMod x 10

nsr[n_] := Numerator[Total[1/Select[IntegerDigits[n], # > 0 &]]]; nsr /@ Range[0, 79] (* Jayanta Basu, Jul 13 2013 *)

a(n) = my(d=digits(n)); numerator(sum(k=1, #d, if (d[k], 1/d[k]))); \\ Michel Marcus, Jan 26 2022

a(A037264(n)) = a(A037268(n)) = a(A214958(n)) = a(A214959(n)) = 1;

a(n) = a(A004719(n)).

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

Original entry on oeis.org

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

Naohiro Nomoto

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

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

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

Cf. A037265, A045910.

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

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 *)

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

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

A214959 Numbers for which the sum of reciprocals of nonzero digits = 1.

Original entry on oeis.org

1, 10, 22, 100, 202, 220, 236, 244, 263, 326, 333, 362, 424, 442, 623, 632, 1000, 2002, 2020, 2036, 2044, 2063, 2200, 2306, 2360, 2404, 2440, 2488, 2603, 2630, 2666, 2848, 2884, 3026, 3033, 3062, 3206, 3260, 3303, 3330, 3366, 3446, 3464, 3602, 3620, 3636

Offset: 1

Reinhard Zumkeller, Aug 02 2012

Intersection of A214957 and A214958: A214949(a(n))*A214950(a(n)) = 1.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A037268 (subsequence).

import Data.Ratio ((%), numerator, denominator)
a214959 n = a214959_list !! (n-1)
a214959_list = [x | x <- [0..], f x 0] where
   f 0 v = numerator v == 1 && denominator v == 1
   f u v | d > 0     = f u' (v + 1 % d)
         | otherwise = f u' v  where (u',d) = divMod u 10

SumReciprocalsDigits:=func; [n: n in [1..3636] | IsOne(SumReciprocalsDigits(n))]; // Bruno Berselli, Aug 02 2012

idnQ[n_]:=Total[1/Select[IntegerDigits[n],#>0&]]==1; Select[Range[ 4000],idnQ] (* Harvey P. Dale, Dec 08 2012 *)

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A214949 Numerator of sum of reciprocals of all nonzero digits of n in decimal representation.

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

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A214959 Numbers for which the sum of reciprocals of nonzero digits = 1.

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