Integer average

Today we will illustrate a new idea with the number 2024.
What digits are absent from 2024? They are the digits 1, 3, 5, 6, 7, 8 and 9.
We sum those seven digits: 1 + 3 + 5 + 6 + 7 + 8 + 9 = 39. 
As 39 is not divisible by seven, we do not accept 2024 in our new sequence.

Giorgos Kalogeropoulos was quick to correct A, extend it and ask the question after the examples:

A = 0, 9, 14, 23, 32, 41, 49, 50, 58, 67, 76, 85, 94, 99, 102, 109, 114, 120, 127, 136, 141, 144, 145, 154, 163, 172, 179, 190, 197, 201, 208, 210, 217, 223, 232, 233, 235, 253, 269, 271, 278, 280, 287, 296, 307, 316, 322, 323, 325, 332, 352, 359, 361, 368, 370, 386, 395, 406, 411, 414, 415, 441, 449, 451, 458, 460, 467, 476, 485, 494, 499, 500, 505, 514, 523, 532, 539, 541, 548, 550, 558, 584, 585, 588, 593, 604, 613, 629, 631, 638, 640, 647, 667, 674, 676, 677, 683, 692, 703, 712, 719, 721, 728, 730, 746, 764, 766, 767, 776, 782, 789, 791, 798, 802, 809, 820, 827, 836, 845, 854, 855, 858, 863, 872, 879, 885, 890, 897, 901, 908, 910, 917, 926, 935, 944, 949, 953, 962, 971, 978, 980, 987, 994, 999...

Examples
 0 is in A because the 9 remaining digits sum up to 45 and 45 is divisible by 9;
 9 is in A because the 9 remaining digits sum up to 36 and 36 is divisible by 9;
14 is in A because the 8 remaining digits sum up to 40 and 40 is divisible by 8;
23 is in A because the 8 remaining digits sum up to 40 and 40 is divisible by 8;
32 is in A because the 8 remaining digits sum up to 40 and 40 is divisible by 8;
41 is in A because the 8 remaining digits sum up to 40 and 40 is divisible by 8;
49 is in A because the 8 remaining digits sum up to 32 and 32 is divisible by 8; etc.
____________________
GK
> But what happens with pandigital numbers like 1234567890? How should we handle division by zero?
ÉA
... Mmmmmh, let me see...


P.-S.
The sequence A061383 ("Arithmetic mean of digits is an integer") is in the OEIS since May 2001.





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