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

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

Author

Reinhard Zumkeller, Aug 02 2012

Keywords

• nonn
• base
• frac

Links

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

Crossrefs

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

Cf. A214949 (numerators).

Programs

Haskell

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

Mathematica

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

PARI

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

Formula

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

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