A117318 Numbers n such that Phi(n,x) is a flat cyclotomic polynomial of order four.

431985, 757335, 865365, 1134915, 1296885, 1297815, 1675365, 1729335, 1891815, 2161785, 2162715, 2595165, 2648715, 2649585, 3027165, 3028035, 3132015, 3133785, 3347985, 3405615, 3565785, 3784065, 3891585, 4698465, 4920285, 5188935, 5189865, 5676315

Offset

1,1

Comments

A flat polynomial is defined to be a polynomial whose coefficients are -1, 0, or 1. Order four means that n is the product of four odd primes p<q<r<s.

For pqrs to be flat, it appears that three conditions on p < q < r < s are required: q = -1 (mod p), r = +-1 (mod pq), and s = +-1 (mod pqr). [T. D. Noe, Apr 13 2010]

Links

T. D. Noe, Table of n, a(n) for n=1..216

Nathan Kaplan, Flat cyclotomic polynomials of order four and higher, #A30, Integers 10 (2010), 357-363.

Carlo Sanna, A Survey on Coefficients of Cyclotomic Polynomials, arXiv:2111.04034 [math.NT], 2021.

Crossrefs

Cf. A117223 (third-order flat cyclotomic polynomials).

Sequence in context: A233620 A271110 A237926 * A085092 A117151 A186048

Adjacent sequences: A117315 A117316 A117317 * A117319 A117320 A117321

Keyword

nonn

Author

T. D. Noe, Mar 07 2006

Status

approved