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

10,5

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

Links

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

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

Example

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.

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

Crossrefs

Cf. A000042.

Sequence in context: A360205 A078909 A067458 * A376252 A347323 A324471

Adjacent sequences: A088327 A088328 A088329 * A088331 A088332 A088333

Keyword

base,nonn,look

Author

Amarnath Murthy, Oct 01 2003

Extensions

More terms from Ray Chandler, Oct 06 2003

Status

approved