Yesterday I turned 28156 days old and this number has an interesting property:$$28156 = 4 \times 7039$$The factorisation shown is not the prime factorisation but, looking at both sides of the equation, it can be seen that each of the digits from 0 to 9 occurs exactly once. This makes the number a member of OEIS A370970:
A370970: numbers \(k\) which have a factorization \(k = f_1 \times f_2 \times \dots \times f_n \) where the digits of \({k, f_1, f_2, \dots, f_n}\) together give \(0,1, \dots ,9\) exactly once.
Here is the complete list of terms:
8596 = 2 x 14 x 307
8790 = 2 x 3 x 1465
9360 = 2 x 4 x 15 x 78
9380 = 2 x 5 x 14 x 67
9870 = 2 x 3 x 1645
10752 = 3 x 4 x 896
12780 = 4 x 5 x 639
14760 = 5 x 9 x 328
14820 = 5 x 39 x 76
15628 = 4 x 3907
15678 = 39 x 402
16038 = 27 x 594 = 54 x 297
16704 = 9 x 32 x 58
17082 = 3 x 5694
17820 = 36 x 495 = 45 x 396
17920 = 8 x 35 x 64
18720 = 4 x 5 x 936
19084 = 52 x 367
19240 = 8 x 37 x 65
20457 = 3 x 6819
20574 = 6 x 9 x 381
20754 = 3 x 6918
21658 = 7 x 3094
24056 = 8 x 31 x 97
24507 = 3 x 8169
25803 = 9 x 47 x 61
26180 = 4 x 7 x 935
26910 = 78 x 345
27504 = 3 x 9168
28156 = 4 x 7039
28651 = 7 x 4093
30296 = 7 x 8 x 541
30576 = 8 x 42 x 91
30752 = 4 x 8 x 961
31920 = 5 x 76 x 84
32760 = 8 x 45 x 91
32890 = 46 x 715
34902 = 6 x 5817
36508 = 4 x 9127
47320 = 8 x 65 x 91
58401 = 63 x 927
65128 = 7 x 9304
65821 = 7 x 9403
These numbers are few and far between as can be seen and 28156 in particular recurs with permuted digits as 15628, 21658, 28651, 65128 and 65821.
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