A088330 Sum of the remainders when n is divided by nonzero numbers obtained by deleting one digit. The sum ranges over all the 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, 3, 8, 16, 10, 5, 20, 14, 12, 24, 0

Offset: 10

Author

Amarnath Murthy, Oct 01 2003

Keywords

• base
• nonn
• look

Comments

Differs from A067458 first at n=101, where A067458(101)=0 and a(101) = (101 mod 1) + (101 mod 11) + (101 mod 10) = 0+2+1 = 3. - R. J. Mathar, Sep 11 2008

Examples

			a(1234) = Rem[1234/123] + Rem[1234/124]+ Rem[1234/134] + Rem[1234/234] = 4+ 118 + 28 + 64 = 214 where Rem [a/b] = the remainder when a is divided by b.
		

Links

• Robert Israel, Table of n, a(n) for n = 10..10000

Crossrefs

Cf. A000042.

Programs

Maple

f:= proc(n) local L,d,i,j,x,t;
     L:= convert(n,base,10); d:= nops(L); t:= 0;
     for i from 1 to d do
       x:= add(L[j]*10^(j-1),j=1..i-1) + add(L[j]*10^(j-2),j=i+1..d);
       if x <> 0 then t:= t + (n mod x) fi;
     od;
     t
end proc:
map(f, [$10 .. 200]); # Robert Israel, Dec 05 2024

Formula

a((10^n - 1)/9) = n. for n > 2. a(1111111 n times ) = a(A000042(n)) = n, n > 2.

a(10 * n) = 10 * a(n). - Robert Israel, Dec 05 2024

Extensions

More terms from Ray Chandler, Oct 06 2003