A214957 -id:A214957 - cp's OEIS frontend

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

Erich Friedman

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

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

Cf. A052382, A168046, A214950, A214957.

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

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 *)

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

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

A214950 Denominator of sum of reciprocals of all nonzero digits of n in decimal representation.

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 2, 1, 6, 4, 10, 3, 14, 8, 18, 3, 3, 6, 3, 12, 15, 2, 21, 24, 9, 4, 4, 4, 12, 2, 20, 12, 28, 8, 36, 5, 5, 10, 15, 20, 5, 30, 35, 40, 45, 6, 6, 3, 2, 12, 30, 3, 42, 24, 18, 7, 7, 14, 21, 28, 35, 42

Offset: 0

Reinhard Zumkeller, Aug 02 2012

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

Cf. A034708, A037268, A214957, A214959, A004719.

Cf. A214949 (numerators).

import Data.Ratio ((%), denominator)
a214950 = f 0 where
   f y 0 = denominator y
   f y x = f (y + if d == 0 then 0 else 1 % d) x'
           where (x',d) = divMod x 10

dsr[n_] := Denominator[Total[1/Select[IntegerDigits[n], # > 0 &]]]; dsr /@ Range[0, 76] (* Jayanta Basu, Jul 13 2013 *)

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

a(A034708(n)) = a(A037268(n)) = a(A214957(n)) = a(A214959(n)) = 1;

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

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 *)

cp's OEIS Frontend

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

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A214950 Denominator of sum of reciprocals of all nonzero digits of n in decimal representation.

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

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