A123104 -id:A123104 - cp's OEIS frontend

A127101 Numbers k such that k^2 divides 9^k - 1.

1, 2, 4, 8, 10, 20, 40, 110, 136, 164, 220, 328, 440, 610, 680, 820, 1210, 1220, 1544, 1640, 2420, 2440, 2530, 4840, 5060, 5576, 6710, 7370, 7480, 7720, 9020, 10120, 11810, 13420, 13612, 14008, 14740, 18040, 18632, 19580

Offset: 1

Alexander Adamchuk, Jan 05 2007

nonn

Amiram Eldar, Table of n, a(n) for n = 1..3000 (terms 1..56 from R. J. Mathar)

Subset of A068382 (numbers k such that k divides 9^k - 1).

Cf. A127100, A127102, A127103, A123104, A127105, A127106, A127107, A127092.

Select[Range[20000], IntegerQ[(PowerMod[9, #, #^2 ]-1)/#^2 ]&]

is(k) = Mod(9, k^2)^k == 1; \\ Amiram Eldar, May 21 2024

A127105 Numbers k such that k^2 divides 5^k-1.

Original entry on oeis.org

1, 2, 4, 6, 12, 42, 52, 84, 156, 186, 372, 1092, 1218, 1302, 1806, 2436, 2604, 2756, 3612, 4836, 5334, 7212, 8268, 10668, 12324, 15918, 18858, 24492, 31668, 31836, 33852, 37716, 37758, 46956, 50484, 52374, 55986, 57876, 71862, 75516, 86268

Offset: 1

Alexander Adamchuk, Jan 05 2007

nonn

Subset of A067946 (numbers k such that k divides 5^k-1).

Robert Israel, Table of n, a(n) for n = 1..1000
Taro Morishima, Über die Fermatsche Vermutung, Proc. Imp. Acad., Volume 4, Number 10 (1928), 590-592.

Cf. A127100, A127101, A127102, A127103, A123104, A127106, A127107, A127092.

Cf. A067946 (numbers k such that k divides 5^k-1).

select(t -> (5 &^t - 1) mod (t^2) = 0, [$1..10^5]); # Robert Israel, Jul 15 2018

Select[Range[30000], IntegerQ[(PowerMod[5, #, #^2 ]-1)/#^2 ]&]

isok(n) = Mod(5, n^2)^n == 1; \\ Michel Marcus, Apr 23 2017

More terms from Ryan Propper and Alexander Adamchuk, Jan 05 2007

A127107 Numbers n such that n^2 divides 7^n-1.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 12, 20, 24, 40, 57, 60, 100, 114, 120, 156, 200, 220, 228, 258, 300, 312, 440, 456, 516, 600, 660, 780, 1032, 1100, 1140, 1320, 1560, 1640, 1752, 1860, 2172, 2200, 2280, 2580, 2964, 3300, 3660, 3720, 3820, 3900, 4344, 4632, 4902, 4920, 5060

Offset: 1

Alexander Adamchuk, Jan 05 2007

nonn

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A127100, A127101, A127102, A127103, A123104, A127105, A127106, A127092. Cf. A067947 = numbers n such that n divides 7^n-1.

Select[Range[10000], IntegerQ[(PowerMod[7, #, #^2 ]-1)/#^2 ]&]

A123142 Number of benzenoids with 23 hexagons, C_(2v) symmetry and containing n carbon atoms.

Original entry on oeis.org

2, 9, 33, 38, 235, 124, 704, 435, 2283, 1437, 6954, 3628, 17864, 9528, 43798, 24237, 106293, 53593, 228216, 104754, 431864, 188701, 760883, 300925, 1212591, 373411, 1536669, 305586, 1298746, 129710, 586556

Offset: 64

Parthasarathy Nambi, Oct 01 2006

nonn

			If n=64 then the number of benzenoids with 23 hexagons with C_(2v) symmetry is 2.
If n=65 then the number of benzenoids with 23 hexagons with C_(2v) symmetry is 9.
If n=66 then the number of benzenoids with 23 hexagons with C_(2v) symmetry is 33.
If n=67 then the number of benzenoids with 23 hexagons with C_(2v) symmetry is 38.
If n=94 then the number of benzenoids with 23 hexagons with C_(2v) symmetry is 586556.

G. Brinkmann, G. Caporossi and P. Hansen, "A Survey and New Results on Computer Enumeration of Polyhex and Fusene Hydrocarbons", J. Chem. Inf. Comput. Sci., vol. 43 (2003) 842-851. See Table 6 column 7 on page 847.

Cf. A122539, A121964, A122736, A123044, A123106, A123105, A123104.

A123284 Number of polyhexes with 24 hexagons, C_(2v) symmetry and containing n carbon atoms.

Original entry on oeis.org

2, 34, 37, 173, 155, 657, 482, 2206, 1334, 6510, 3315, 18208, 7804, 47329, 16914, 114779, 33879, 258280, 60786, 532865, 98070, 987689, 137195, 1641862, 166882, 2358366, 146898, 2723100, 77267, 2164650, 0, 966300

Offset: 67

Parthasarathy Nambi, Oct 10 2006

a(98) = 966300 is the last nonzero term. Sum(a(n)) = 12574028 = A120991(24). - Markus Voege, Jan 23 2014

			If n=67 then the number of polyhexes with 24 hexagons with C_(2v) symmetry is 2.
If n=68 then the number of polyhexes with 24 hexagons with C_(2v) symmetry is 34.
If n=69 then the number of polyhexes with 24 hexagons with C_(2v) symmetry is 37.
If n=70 then the number of polyhexes with 24 hexagons with C_(2v) symmetry is 173.

G. Brinkmann, G. Caporossi and P. Hansen, A Survey and New Results on Computer Enumeration of Polyhex and Fusene Hydrocarbons, J. Chem. Inf. Comput. Sci., vol. 43 (2003) 842-851. See Table 7 column 7 on page 848.

Cf. A120991, A122539, A121964, A122736, A123044, A123106, A123105, A123104, A123142.

Series corrected a(97)=0 and a(98)=966300; keyword 'fini' by Markus Voege, Jan 23 2014

A123285 Number of fusenes with 22 hexagons, C_(3h) symmetry and containing 3n carbon atoms.

Original entry on oeis.org

1, 2, 8, 21, 60, 160, 281, 655, 1003, 1102

Offset: 21

Parthasarathy Nambi, Oct 10 2006

G. Brinkmann, G. Caporossi and P. Hansen, A Survey and New Results on Computer Enumeration of Polyhex and Fusene Hydrocarbons, J. Chem. Inf. Comput. Sci., vol. 43 (2003) 842-851. See Table 8 column 4 on page 848.

Cf. A122539, A121964, A122736, A123044, A123106, A123105, A123104, A123142.

Name and offset edited by Andrey Zabolotskiy, Nov 15 2023

A123286 Number of fusenes with 22 hexagons, D_(2h) symmetry and containing 2n carbon atoms.

Original entry on oeis.org

1, 3, 3, 6, 17, 19, 26, 32, 40, 54, 131, 70, 277, 51, 188

Offset: 31

Parthasarathy Nambi, Oct 10 2006

G. Brinkmann, G. Caporossi and P. Hansen, A Survey and New Results on Computer Enumeration of Polyhex and Fusene Hydrocarbons, J. Chem. Inf. Comput. Sci., vol. 43 (2003) 842-851. See Table 8 column 5 on page 848.

Cf. A122539, A121964, A122736, A123044, A123106, A123105, A123104, A123142.

Name and offset edited by Andrey Zabolotskiy, Nov 15 2023

A123287 Number of fusenes with 22 hexagons, C_(2h) symmetry and containing 2n carbon atoms.

Original entry on oeis.org

2, 32, 138, 510, 1630, 4757, 13276, 34345, 81379, 173257, 332556, 549920, 737676, 683310, 375524

Offset: 31

Parthasarathy Nambi, Oct 10 2006

G. Brinkmann, G. Caporossi and P. Hansen, A Survey and New Results on Computer Enumeration of Polyhex and Fusene Hydrocarbons, J. Chem. Inf. Comput. Sci., vol. 43 (2003) 842-851. See Table 8 column 6 on page 848.

Cf. A122539, A121964, A122736, A123044, A123106, A123105, A123104, A123142.

Name and offset edited by Andrey Zabolotskiy, Nov 15 2023

A123288 Number of fusenes with 22 hexagons, C_(2v) symmetry and containing n carbon atoms.

Original entry on oeis.org

4, 8, 56, 54, 212, 187, 783, 533, 2535, 1352, 7484, 3391, 21245, 8067, 55794, 16692, 135190, 31411, 291344, 52815, 574364, 76282, 971115, 76761, 1342969, 51319, 1274425, 0, 751033

Offset: 62

Parthasarathy Nambi, Oct 10 2006

G. Brinkmann, G. Caporossi and P. Hansen, A Survey and New Results on Computer Enumeration of Polyhex and Fusene Hydrocarbons, J. Chem. Inf. Comput. Sci., vol. 43 (2003) 842-851. See Table 8 column 7 on page 848.

Cf. A122539, A121964, A122736, A123044, A123106, A123105, A123104, A123142.

a(89) = 0 inserted by Andrey Zabolotskiy, Nov 09 2023

A123289 Number of fusenes with 23 hexagons, D_(2h) symmetry and containing 2n carbon atoms.

Original entry on oeis.org

1, 3, 3, 6, 13, 19, 28, 37, 55, 92, 91, 139, 114, 256, 0, 188

Offset: 32

Parthasarathy Nambi, Oct 10 2006

G. Brinkmann, G. Caporossi and P. Hansen, A Survey and New Results on Computer Enumeration of Polyhex and Fusene Hydrocarbons, J. Chem. Inf. Comput. Sci., vol. 43 (2003) 842-851. See Table 9 column 5 on page 849.

Cf. A122539, A121964, A122736, A123044, A123106, A123105, A123104, A123142.

Name and offset corrected and a(46) = 0 inserted by Andrey Zabolotskiy, Nov 09 2023

cp's OEIS Frontend

A127101 Numbers k such that k^2 divides 9^k - 1.

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A127105 Numbers k such that k^2 divides 5^k-1.

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A127107 Numbers n such that n^2 divides 7^n-1.

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A123142 Number of benzenoids with 23 hexagons, C_(2v) symmetry and containing n carbon atoms.

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A123284 Number of polyhexes with 24 hexagons, C_(2v) symmetry and containing n carbon atoms.

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A123285 Number of fusenes with 22 hexagons, C_(3h) symmetry and containing 3n carbon atoms.

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A123286 Number of fusenes with 22 hexagons, D_(2h) symmetry and containing 2n carbon atoms.

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A123287 Number of fusenes with 22 hexagons, C_(2h) symmetry and containing 2n carbon atoms.

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A123288 Number of fusenes with 22 hexagons, C_(2v) symmetry and containing n carbon atoms.

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Author

Keywords

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Extensions

A123289 Number of fusenes with 23 hexagons, D_(2h) symmetry and containing 2n carbon atoms.

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Author

Keywords

Links

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