Minimum multiple of m where digital sum equals m

Minimum multiple of m where digital sum equals m is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Generate the sequence a(n) when each n is the minimum integer multiple m such that the digit sum of n times m is equal to n.

Task

• Find the first 40 elements of the sequence.

Stretch

• Find the next 30 elements of the sequence.

See also

• [oeis:A131382|OEIS:A131382 - Minimal number m such that Sum_digits(n*m)=n]

Raku

<lang perl6>sub min-mult-dsum ($n) { (1..∞).first: (* × $n).comb.sum == $n }

say .fmt("%2d: ") ~ .&min-mult-dsum for flat 1..40, 41..70;</lang>

Output:

 1: 1
 2: 1
 3: 1
 4: 1
 5: 1
 6: 1
 7: 1
 8: 1
 9: 1
10: 19
11: 19
12: 4
13: 19
14: 19
15: 13
16: 28
17: 28
18: 11
19: 46
20: 199
21: 19
22: 109
23: 73
24: 37
25: 199
26: 73
27: 37
28: 271
29: 172
30: 1333
31: 289
32: 559
33: 1303
34: 847
35: 1657
36: 833
37: 1027
38: 1576
39: 1282
40: 17497
41: 4339
42: 2119
43: 2323
44: 10909
45: 11111
46: 12826
47: 14617
48: 14581
49: 16102
50: 199999
51: 17449
52: 38269
53: 56413
54: 37037
55: 1108909
56: 142498
57: 103507
58: 154981
59: 150661
60: 1333333
61: 163918
62: 322579
63: 315873
64: 937342
65: 1076923
66: 1030303
67: 880597
68: 1469116
69: 1157971
70: 12842857