A152942 -id:A152942 - cp's OEIS frontend

A152955 Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) has height 1.

1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 29, 31, 33, 35, 37, 39, 41, 43, 47, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 91, 93, 95, 97, 101, 103, 107, 109, 111, 113, 115, 119, 123, 127, 129, 131, 133, 137, 139, 141, 143, 145, 149, 151, 155, 157

Offset: 1

T. D. Noe, Dec 16 2008

nonn

The height of a polynomial is the maximum of the absolute value of its coefficients. Polynomials of height 1 are also called flat polynomials. This sequence includes prime (first order) and semiprime (second order) n, as well as third-order (A117223), fourth-order (A117318) and higher-order n.

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A152940, A152941, A152942, A152943.

is(n)=issquarefree(n) && n%2 && vecmax(abs(Vec(polcyclo(n))))==1 \\ Charles R Greathouse IV, Nov 05 2017

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

T. D. Noe, Jan 09 2009

nonn

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.

T. D. Noe, Table of n, a(n) for n = 1..1000

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

Select[Range[2000], OddQ[#] && SquareFreeQ[#] && Max[ Abs[ CoefficientList[ Cyclotomic[#, x], x]]] > 1&] (* Jean-François Alcover, Nov 14 2016 *)

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

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

nonn

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

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A152955, A152941, A152942, A152943.

is(n)=issquarefree(n) && n%2 && vecmax(abs(Vec(polcyclo(n))))==2 \\ Charles R Greathouse IV, Nov 05 2017

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

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

nonn

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

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A152955, A152940, A152942, A152943.

is(n)=issquarefree(n) && n%2 && vecmax(abs(Vec(polcyclo(n))))==3 \\ Charles R Greathouse IV, Nov 05 2017

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

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

nonn

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

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A152955, A152940, A152941, A152942.

is(n)=issquarefree(n) && n%2 && vecmax(abs(Vec(polcyclo(n))))==5 \\ Charles R Greathouse IV, Nov 05 2017

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

Max Alekseyev, May 19 2006

nonn

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

T. D. Noe, Table of n, a(n) for n=1..1000

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

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A152955 Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) has height 1.

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

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

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

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

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

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