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

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

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

Table of n, a(n) for n=10..110.

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.

Crossrefs

Cf. A000042.

Sequence in context: A360205 A078909 A067458 * A347323 A324471 A346576

Adjacent sequences: A088327 A088328 A088329 * A088331 A088332 A088333

Keyword

base,nonn

Author

Amarnath Murthy, Oct 01 2003

Extensions

More terms from Ray Chandler, Oct 06 2003

Status

approved