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 1-7 of 7 results.

A154430 Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) has height > 1.

Original entry on oeis.org

105, 165, 195, 255, 273, 285, 345, 357, 385, 429, 455, 555, 561, 595, 609, 615, 627, 645, 665, 705, 715, 759, 777, 795, 805, 897, 935, 957, 969, 987, 1001, 1005, 1015, 1023, 1045, 1065, 1085, 1095, 1105, 1131, 1155, 1185, 1221, 1235, 1239, 1245, 1265
Offset: 1

Views

Author

T. D. Noe, Jan 09 2009

Keywords

Comments

The height of a polynomial is the maximum of the absolute value of its coefficients. Different from A118678, which excludes terms that are a multiple of smaller terms.

Links

Crossrefs

Cf. A013590, A117318, A117223, A152940, A152941, A152942, A152943, A152955.

Programs

  • Mathematica
    Select[Range[2000], OddQ[#] && SquareFreeQ[#] && Max[ Abs[ CoefficientList[ Cyclotomic[#, x], x]]] > 1&] (* Jean-François Alcover, Nov 14 2016 *)
  • PARI
    is(n)=issquarefree(n) && n%2 && vecmax(abs(Vec(polcyclo(n))))>1 \\ Charles R Greathouse IV, Nov 05 2017

A152940 Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) has height 2.

Original entry on oeis.org

105, 165, 195, 255, 273, 285, 345, 357, 429, 455, 555, 561, 609, 615, 627, 645, 705, 715, 759, 777, 795, 805, 897, 957, 969, 987, 1001, 1005, 1015, 1023, 1045, 1065, 1085, 1095, 1105, 1131, 1185, 1221, 1239, 1245, 1265, 1295, 1407, 1419, 1435, 1455, 1491
Offset: 1

Views

Author

T. D. Noe, Dec 16 2008, Jan 09 2009

Keywords

Comments

The height of a polynomial is the maximum of the absolute value of its coefficients. Subsequence of A154430.

Links

Crossrefs

Cf. A152955, A152941, A152942, A152943.

Programs

A152941 Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) has height 3.

Original entry on oeis.org

385, 595, 665, 935, 1155, 1235, 1309, 1463, 1495, 1729, 1855, 1955, 2065, 2261, 2465, 2665, 2795, 2821, 3045, 3059, 3115, 3145, 3289, 3451, 3619, 3655, 3857, 4123, 4277, 4389, 4403, 4433, 4669, 4697, 4745, 4807, 4879, 4935, 4945, 5015, 5083, 5117, 5285
Offset: 1

Views

Author

T. D. Noe, Dec 16 2008, Jan 09 2008

Keywords

Comments

The height of a polynomial is the maximum of the absolute value of its coefficients. Subsequence of A154430.

Links

Crossrefs

Cf. A152955, A152940, A152942, A152943.

Programs

A152942 Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) has height 4.

Original entry on oeis.org

1365, 1995, 2415, 2431, 2737, 2849, 3003, 3255, 3315, 3553, 3689, 4081, 4147, 4199, 4305, 4485, 4515, 4543, 4991, 5593, 5681, 5865, 6045, 6105, 6251, 6405, 6409, 6555, 6721, 6851, 7049, 7395, 7469, 7665, 7667, 7755, 7777, 7905, 8547, 8715, 8835, 9165
Offset: 1

Views

Author

T. D. Noe, Dec 16 2008, Jan 09 2009

Keywords

Comments

The height of a polynomial is the maximum of the absolute value of its coefficients. Subsequence of A154430.

Links

Crossrefs

Cf. A152955, A152940, A152941, A152943.

Programs

A152943 Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) has height 5.

Original entry on oeis.org

1785, 2145, 2717, 3705, 3795, 3885, 3927, 4785, 4845, 5005, 5115, 5187, 5291, 5313, 5655, 6765, 7035, 7215, 7293, 8211, 8265, 8385, 8569, 8855, 9269, 9435, 9735, 9867, 10065, 10545, 10659, 10857, 10965, 11055, 11339, 11685, 12243, 12597, 12673
Offset: 1

Views

Author

T. D. Noe, Dec 16 2008, Jan 09 2009

Keywords

Comments

The height of a polynomial is the maximum of the absolute value of its coefficients. Subsequence of A154430.

Links

Crossrefs

Cf. A152955, A152940, A152941, A152942.

Programs

A118678 Primitive orders of cyclotomic polynomials containing a coefficient with absolute value >= 2.

Original entry on oeis.org

105, 165, 195, 255, 273, 285, 345, 357, 385, 429, 455, 555, 561, 595, 609, 615, 627, 645, 665, 705, 715, 759, 777, 795, 805, 897, 935, 957, 969, 987, 1001, 1005, 1015, 1023, 1045, 1065, 1085, 1095, 1105, 1131, 1185, 1221, 1235, 1239, 1245, 1265, 1295
Offset: 1

Views

Author

Max Alekseyev, May 19 2006

Keywords

Comments

All elements of A013590 with no proper divisors belonging to A013590.

Links

Crossrefs

Cf. A013590, A117318, A117223.
Cf. A152940, A152941, A152942, A152943, A152955
Cf. A154430

A374137 Odd numbers k such that the cyclotomic polynomial Phi(k,x) has height 1, i.e., whose coefficients are all -1, 0, or 1.

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151
Offset: 1

Views

Author

Antti Karttunen, Jul 06 2024

Keywords

Links

Crossrefs

Cf. A374136 (characteristic function).
Setwise difference A005408 \ A013590.
Subsequences: A152955, A117223, A117318.
Appears to be a subsequence of A089684, from which this differs for the first time at n=125, where a(125) = 257, which misses A089684(125) = 255.

Programs

Showing 1-7 of 7 results.

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