cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 14 results. Next

A070528 Number of divisors of 10^n-1 (999...999 with n digits).

Original entry on oeis.org

3, 6, 8, 12, 12, 64, 12, 48, 20, 48, 12, 256, 24, 48, 128, 192, 12, 640, 6, 384, 256, 288, 6, 2048, 96, 192, 96, 768, 96, 16384, 24, 6144, 128, 192, 384, 5120, 24, 24, 128, 6144, 48, 49152, 48, 4608, 1280, 192, 12, 16384, 48, 3072, 512, 1536, 48, 12288, 768
Offset: 1

Views

Author

Henry Bottomley, May 02 2002

Keywords

Examples

			a(7)=12 since the divisors of 9999999 are 1, 3, 9, 239, 717, 2151, 4649, 13947, 41841, 1111111, 3333333, 9999999.

Links

Crossrefs

Cf. A004023 (indices of 6's).
Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895.
Cf. A046801, A005422, A102347, A046053, A057951, A007138, A003060, A059892, A085035.

Programs

  • Mathematica
    DivisorSigma[0,#]&/@(10^Range[60]-1) (* Harvey P. Dale, Jan 14 2011 *)
Table[DivisorSigma[0, 10^n - 1], {n, 60}] (* T. D. Noe, Aug 18 2011 *)
  • PARI
    a(n) = numdiv(10^n - 1); \\ Michel Marcus, Sep 08 2015

Formula

a(n) = A000005(A002283(n)).
a(n) = Sum_{d|n} A059892(d).
a(n) = A070529(n)*(A007949(n)+3)/(A007949(n)+1).

Extensions

Terms to a(280) in b-file from Hans Havermann, Aug 19 2011
a(281)-a(322) in b-file from Ray Chandler, Apr 22 2017
a(323)-a(352) in b-file from Max Alekseyev, May 04 2022

A106305 Divisors of 10^14 - 1.

Original entry on oeis.org

1, 3, 9, 11, 33, 99, 239, 717, 2151, 2629, 4649, 7887, 13947, 23661, 41841, 51139, 153417, 460251, 909091, 1111111, 2727273, 3333333, 8181819, 9999999, 10000001, 12222221, 30000003, 36666663, 90000009, 109999989, 217272749, 651818247
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 12 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A001270, A007138, A046107, A112505.

Programs

Formula

10^14 - 1 = 3^2 * 11 * 239 * 4649 * 909091 = 99999999999999. - Alonso del Arte, Nov 09 2017

A109492 Divisors of 111111.

Original entry on oeis.org

1, 3, 7, 11, 13, 21, 33, 37, 39, 77, 91, 111, 143, 231, 259, 273, 407, 429, 481, 777, 1001, 1221, 1443, 2849, 3003, 3367, 5291, 8547, 10101, 15873, 37037, 111111
Offset: 1

Views

Author

Philippe Deléham, Aug 28 2005

Keywords

Comments

Note that the smaller repunits R3=111, R4=1111, R5=11111 are semiprimes and have only 4 divisors, which is again the case for the next repunit R7=1111111. - M. F. Hasler, Oct 13 2011

Links

Crossrefs

Cf. A070529, A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895. [M. F. Hasler, Oct 13 2011]
Cf. A199799 (totatives of 111111), A154549 (111111*n).

Programs

A069105 1/n has period 3 in base 10.

Original entry on oeis.org

27, 37, 54, 74, 108, 111, 135, 148, 185, 216, 222, 270, 296, 333, 370, 432, 444, 540, 555, 592, 666, 675, 740, 864, 888, 925, 999, 1080, 1110, 1184, 1332, 1350, 1480, 1665, 1728, 1776, 1850, 1998, 2160, 2220, 2368, 2664, 2700, 2775, 2960, 3330, 3375, 3456, 3552, 3700, 3996, 4320, 4440, 4625, 4736, 4995
Offset: 1

Views

Author

Joshua Horowitz (mccartneyman(AT)yahoo.com), Apr 07 2002

Keywords

Examples

			1/1332 = 0.000750750750...

Links

Crossrefs

Cf. A018766, A003592, A070021, A070022, A070023.

Programs

  • Mathematica
    Select[ Range[7500], Length[ RealDigits[1/# ] [[1, -1]]] == 3 &]
  • PARI
    is(n,S=[27,37,111,333,999])=setsearch(S,n\5^valuation(n,5)>>valuation(n,2)) \\ M. F. Hasler, Apr 25 2017

Formula

Numbers of the form a*b*c where a is in {27, 37, 111, 333, 999}, b is a power of 2 and c is a power of 5. - Henry Bottomley, Apr 12 2002
Equivalently: A132740(n) divides 999 but does not divide 9. - M. F. Hasler, Apr 25 2017

Extensions

Extended by Robert G. Wilson v, Apr 07 2002
Terms added and program corrected to agree with description by Ray Chandler, Apr 17 2017

A109933 Divisors of 10^13 - 1.

Original entry on oeis.org

1, 3, 9, 53, 79, 159, 237, 477, 711, 4187, 12561, 37683, 265371653, 796114959, 2388344877, 14064697609, 20964360587, 42194092827, 62893081761, 126582278481, 188679245283, 1111111111111, 3333333333333, 9999999999999
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 11 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A001270, A007138, A046107.

Programs

A111117 Divisors of 10^15 - 1.

Original entry on oeis.org

1, 3, 9, 27, 31, 37, 41, 93, 111, 123, 271, 279, 333, 369, 813, 837, 999, 1107, 1147, 1271, 1517, 2439, 3441, 3813, 4551, 7317, 8401, 10027, 10323, 11111, 11439, 13653, 25203, 30081, 30969, 33333, 34317, 40959, 47027, 75609, 90243, 99999, 141081
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 15 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A001270, A007138, A046107, A112505.

Programs

A111211 Divisors of 10^16 - 1.

Original entry on oeis.org

1, 3, 9, 11, 17, 33, 51, 73, 99, 101, 137, 153, 187, 219, 303, 411, 561, 657, 803, 909, 1111, 1233, 1241, 1507, 1683, 1717, 2329, 2409, 3333, 3723, 4521, 5151, 6987, 7227, 7373, 9999, 10001, 11169, 13563, 13651, 13837, 15453, 18887, 20961, 22119, 25619
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 25 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A001270, A007138, A046107, A112505.

Programs

A113522 Divisors of 10^18 - 1.

Original entry on oeis.org

1, 3, 7, 9, 11, 13, 19, 21, 27, 33, 37, 39, 57, 63, 77, 81, 91, 99, 111, 117, 133, 143, 171, 189, 209, 231, 247, 259, 273, 297, 333, 351, 399, 407, 429, 481, 513, 567, 627, 693, 703, 741, 777, 819, 891, 999, 1001, 1053, 1197, 1221, 1287, 1443, 1463, 1539, 1729
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jan 12 2006

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A111211, A113116, A001270, A007138, A046107, A112505.

Programs

A113116 Divisors of 10^17 - 1.

Original entry on oeis.org

1, 3, 9, 2071723, 6215169, 18645507, 5363222357, 16089667071, 48269001213, 11111111111111111, 33333333333333333, 99999999999999999
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jan 02 2006

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A111211, A001270, A007138, A046107, A112505.

Programs

A197308 Divisors of 11111111.

Original entry on oeis.org

1, 11, 73, 101, 137, 803, 1111, 1507, 7373, 10001, 13837, 81103, 110011, 152207, 1010101, 11111111
Offset: 1

Views

Author

M. F. Hasler, Oct 13 2011

Keywords

Links

Crossrefs

Cf. A109492, A197309, A070529, A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895.

Programs

  • Mathematica
    Divisors[11111111] (* Harvey P. Dale, Nov 12 2021 *)
  • PARI
    divisors(11111111)
Showing 1-10 of 14 results. Next

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