A113522 -id:A113522 - cp's OEIS frontend

A226477 Table (read by rows) of the natural numbers (in ascending order) whose reciprocals have only periodic decimals of length k.

1, 3, 9, 11, 33, 99, 27, 37, 111, 333, 999, 101, 303, 909, 1111, 3333, 9999, 41, 123, 271, 369, 813, 2439, 11111, 33333, 99999, 7, 13, 21, 39, 63, 77, 91, 117, 143, 189, 231, 259, 273, 297, 351, 407, 429, 481, 693, 777, 819, 1001, 1221, 1287, 1443, 2079, 2331, 2457, 2849, 3003, 3367, 3663, 3861, 4329, 5291, 6993, 8547, 9009, 10101, 10989, 12987, 15873, 25641, 27027, 30303, 37037, 47619, 76923, 90909, 111111, 142857, 333333, 999999

Offset: 1

Martin Renner, Jun 08 2013

The k-th row always ends with 10^k - 1 = 99..99 (k times 9).

The number of elements in row k is A059892(k).

			The table T(k,m), m = 1..A059892(k), begins
  1, 3, 9;
  11, 33, 99;
  27, 37, 111, 333, 999;
  etc.

Jianing Song, Rows n = 1..32, flattened

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A111211, A113116, A113522 (Divisors of 10^k - 1, k = 2..18), A059892, A084680.

a:=[1,3,9]: S:={1,3,9}: for k from 2 to 6 do T:=numtheory[divisors](10^k-1): a:=[op(a),op(T minus S)]: S:=S union T; od: a;

Row(n) = my(v=divisors(10^n-1)); select(x->(znorder(Mod(10,x))==n), v) \\ Jianing Song, Jun 15 2021

A245029 Divisors of 3^36 - 1.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 19, 20, 26, 28, 35, 37, 38, 40, 52, 56, 65, 70, 73, 74, 76, 80, 91, 95, 104, 112, 130, 133, 140, 146, 148, 152, 182, 185, 190, 208, 247, 259, 260, 266, 280, 292, 296, 304, 364, 365, 370, 380, 455, 481, 494, 511, 518, 520

Offset: 1

Bruno Berselli, Jul 10 2014

Also, divisors of 9^18-1. Number of divisors of k^18-1 for k = 2..20: 32 (2), 128 (3), 512 (4), 512 (5), 128 (6), 640 (7), 160 (8), 1280 (9), 640 (10), 1024 (11), 512 (12), 2048 (13), 1024 (14), 1536 (15), 8192 (16), 3840 (17), 512 (18), 5120 (19), 512 (20).

			150094635296999120 = 2^4 * 5 * 7 * 13 * 19 * 37 * 73 * 757 * 530713.

Bruno Berselli, Table of n, a(n) for n = 1..1280
Index entries for sequences related to divisors of numbers

Cf. A018614: divisors of 3^6-1.

Cf. A113522: divisors of 10^18-1; A003543: divisors of 2^36-1.

Magma
```
Divisors(3^36-1);
```
Mathematica
```
Divisors[3^36 - 1]
```
Maxima
```
divisors(3^36-1);
```
PARI
```
divisors(3^36-1)
```
Sage
```
divisors(3^36-1)
```

cp's OEIS Frontend

A226477 Table (read by rows) of the natural numbers (in ascending order) whose reciprocals have only periodic decimals of length k.

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