A067458 Sum of remainders when n is divided by its nonzero digits.

0, 0, 0, 1, 2, 0, 4, 3, 2, 1, 0, 1, 0, 3, 0, 1, 2, 7, 4, 3, 0, 1, 2, 0, 3, 2, 0, 3, 8, 3, 0, 1, 2, 4, 0, 1, 6, 8, 0, 5, 0, 1, 2, 5, 6, 0, 3, 3, 5, 9, 0, 1, 2, 3, 4, 5, 0, 5, 6, 9, 0, 1, 2, 4, 6, 5, 10, 0, 7, 9, 0, 1, 2, 5, 4, 5, 8, 10, 0, 9, 0, 1, 2, 3, 6, 5, 6, 13, 10, 0, 0

Offset: 10

Author

Amarnath Murthy, Feb 07 2002

Keywords

• base
• easy
• nonn

Comments

a(n) = 0 for 0 < n 10.

a(A002796(n)) = 0; a(A171492(n)) > 0. - Reinhard Zumkeller, Sep 24 2015

Examples

			a(14)= 2 as 1 divides 14 and 2 is the remainder obtained when 14 is divided by 4.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 10..10000

Crossrefs

Cf. A002796, A171492.

Programs

Haskell

a067458 n = f 0 n where
   f y 0 = y
   f y x = if d == 0 then f y x' else f (y + mod n d) x'
           where (x', d) = divMod x 10
-- Reinhard Zumkeller, Sep 24 2015

Mathematica

Table[Plus @@ Mod[n, Select[IntegerDigits[n], # != 0 &]], {n, 10, 100}]

Extensions

Edited and extended by Robert G. Wilson v, Feb 11 2002