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.

Previous Showing 11-16 of 16 results.

A177915 Numbers k such that k^3 divides 15^(k^2) - 1.

Original entry on oeis.org

1, 2, 4, 7, 8, 14, 16, 28, 56, 68, 112, 136, 226, 272, 406, 452, 476, 812, 904, 952, 1582, 1624, 1808, 1904, 2056, 2758, 3164, 3248, 4112, 5516, 5956, 6328, 7684, 9316, 11032, 11912, 12656, 13804, 14392, 15368, 18632, 21512, 22064, 23824, 23954, 25144
Offset: 1

Views

Author

Alexander Adamchuk, May 14 2010

Keywords

Links

Crossrefs

Cf. A129211, A129212, A177905, A127106, A177907, A127102, A177909, A177243.
Cf. A177911, A177912, A177913, A177914, A177915, A177916, A177917, A177918, A177919, A177920.

Programs

  • Mathematica
    Join[{1}, Select[Range[30000], PowerMod[15, #^2, #^3] == 1 &]] (* Robert Price, Apr 04 2020 *)

A177918 Numbers k such that k^3 divides 18^(k^2) - 1.

Original entry on oeis.org

1, 17, 343927, 1414961, 28626075991, 610559655569, 5417488064959
Offset: 1

Views

Author

Alexander Adamchuk, May 14 2010

Keywords

Comments

17 divides a(n) for n > 1.

Crossrefs

Cf. A128358 (k divides 18^k - 1), A128398 (k^2 divides 18^k - 1).
Cf. A129211, A129212, A177905, A127106, A177907, A127102, A177909, A177243.
Cf. A177911, A177912, A177913, A177914, A177915, A177916, A177917, A177918, A177919, A177920.

Programs

  • Mathematica
    Select[Range[350000], Mod[PowerMod[18, #^2, #^3] - 1, #^3] == 0 &] (* Julien Kluge, Sep 20 2016 *)

Extensions

Three more terms from Max Alekseyev, Oct 02 2010

A177919 Numbers k such that k^3 divides 19^(k^2) - 1.

Original entry on oeis.org

1, 2, 3, 4, 6, 9, 10, 12, 18, 20, 30, 36, 42, 60, 68, 78, 84, 90, 110, 126, 156, 180, 204, 210, 220, 222, 234, 252, 294, 330, 340, 362, 381, 390, 420, 438, 444, 468, 546, 588, 612, 630, 654, 660, 666, 724, 762, 780, 820, 876, 882, 930, 990, 1010, 1014, 1020
Offset: 1

Views

Author

Alexander Adamchuk, May 14 2010

Keywords

Links

Crossrefs

Cf. A129211, A129212, A177905, A127106, A177907, A127102, A177909, A177243.
Cf. A177911, A177912, A177913, A177914, A177915, A177916, A177917, A177918, A177919, A177920.

Programs

  • Mathematica
    Select[ Range[10^4], Mod[ PowerMod[ 19, #^2, #^3 ] - 1, #^3 ] == 0 &]

A218087 Numbers that are divisible by the sum of their digits in every base from 2 through to 16.

Original entry on oeis.org

1, 2, 4, 6, 720, 780, 840, 1008, 1092, 1584, 2016, 2520, 2880, 3168, 3360, 3600, 4368, 5640, 6048, 6720, 7560, 8640, 8820, 9520, 10080, 11088, 12240, 13104, 13440, 13860, 14040, 15840, 17160, 18480, 18720, 19320, 19656, 20736, 21840, 22176, 22680, 23040
Offset: 1

Views

Author

Arkadiusz Wesolowski, Oct 20 2012

Keywords

Comments

Many terms, including the first nine, are in A128397; it seems that the same (and no others(?)) are in A177917. - M. F. Hasler, Oct 21 2012

Examples

			In base 10 the number 322 is divisible by the sum of its digits, it is a Harshad number. It also has this property in octal (322 = 502(8), 5 + 0 + 2 = 7) and hexadecimal (322 = 142(16), 1 + 4 + 2 = 7), but not in binary. Therefore 322 is not a term.

Links

Crossrefs

See A005349 for numbers that are Harshad in base 10.

Programs

  • Mathematica
    lst = {}; Do[b = 2; While[b < 17, If[! Mod[n, Total@IntegerDigits[n, b]] == 0, Break[]]; b++]; If[b == 17, AppendTo[lst, n]], {n, 2, 23040, 2}]; Prepend[lst, 1]
Select[Range[25000],Union[Divisible[#,Table[Total[IntegerDigits[#,b]],{b,2,16}]]]=={True}&] (* Harvey P. Dale, Jan 03 2024 *)

A177908 Integers n such that n^3 divides 8^(n^2) - 1.

Original entry on oeis.org

1, 7, 889, 2359, 299593, 2033143, 13549249, 42931441, 100170217, 188097287, 233727361, 310935751, 685169191, 1515836567, 3606045247, 4566096913, 5452293007, 6620620783, 12721617559, 13162910047, 24088984969, 29683374847, 30987132463, 63388785719, 65576560063, 92349997537
Offset: 1

Views

Author

Max Alekseyev, May 17 2010

Keywords

Comments

Contains A127102 as a subsequence.
From M. F. Hasler, Nov 21 2018: (Start)
The first terms not in A127102 are a({10, 11, 14, 20, 21, 22, ...}) = {188097287, 233727361, 1515836567, 13162910047, 24088984969, 29683374847, ...}.
The listed terms are all squarefree, and all but the first two terms appear to be divisible by either a(3) = 7*127 or a(4) = 7*337. Are there exceptions to these properties? (End)

Crossrefs

Cf. A129211, A129212, A177905, A177907, A177909, A177243, A177911, A177912, A177913, A177914, A177915, A177916, A177917, A177918, A177919, A177920.

Programs

  • Mathematica
    Select[Range[2 10^5], IntegerQ[(8^(#^2) - 1) / #^3] &] (* or *) Select[Range[2 10^6], IntegerQ[(PowerMod[8, #, #^2] - 1) / #^3] &] (* Vincenzo Librandi, Nov 23 2018 *)
  • PARI
    is(n)=Mod(8,n^3)^n^2==1 \\ M. F. Hasler, Nov 21 2018

Extensions

a(23)-a(26) from Giovanni Resta, Nov 23 2018

A177906 Numbers k such that k^3 divides 6^(k^2) - 1.

Original entry on oeis.org

1, 5, 1555, 9673655, 24181805, 90993505, 200928005, 28298980055, 36850702555, 62488609555, 141377087255, 150435008905, 367279622065, 2256331679135, 7521049172905, 18802586659555, 24599612913355, 54706615318945
Offset: 1

Views

Author

Alexander Adamchuk, May 16 2010

Keywords

Comments

5 divides a(n) for n > 1.
Prime divisors of a(n) in order of their appearance are {5, 311, 6221, 15551, 18198701, 40185601, ...}.
From there on, the list is no longer increasing; it continues with 23698201, 90917741, 236192683, 93307, 311021, ... - M. F. Hasler, Oct 21 2012

Crossrefs

Cf. A014946 (k divides 6^k-1), A127106 (k^2 divides 6^k-1).
Cf. A129211, A129212, A177905, A177907, A127102, A177909, A177243.
Cf. A177911, A177912, A177913, A177914, A177915, A177916, A177917, A177918, A177919, A177920.

Programs

Extensions

More terms from Max Alekseyev, Oct 02 2010
Previous Showing 11-16 of 16 results.

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