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Sum of remainders when n is divided by its nonzero digits.
4

%I #6 Sep 24 2015 17:10:33

%S 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,

%T 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,

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

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

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

%C a(A002796(n)) = 0; a(A171492(n)) > 0. - _Reinhard Zumkeller_, Sep 24 2015

%H Reinhard Zumkeller, <a href="/A067458/b067458.txt">Table of n, a(n) for n = 10..10000</a>

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

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

%o (Haskell)

%o a067458 n = f 0 n where

%o f y 0 = y

%o f y x = if d == 0 then f y x' else f (y + mod n d) x'

%o where (x', d) = divMod x 10

%o -- _Reinhard Zumkeller_, Sep 24 2015

%Y Cf. A002796, A171492.

%K base,easy,nonn

%O 10,5

%A _Amarnath Murthy_, Feb 07 2002

%E Edited and extended by _Robert G. Wilson v_, Feb 11 2002