A160355 Odd indices pqr of flat cyclotomic polynomials of order 3 which are not of the form r = +/-1 (mod pq).

231, 399, 483, 651, 663, 741, 1113, 1173, 1209, 1281, 1311, 1353, 1443, 1479, 1533, 1581, 1599, 1653, 1833, 1947, 2163, 2247, 2301, 2337, 2379, 2409, 2829, 2877, 2915, 3129, 3297, 3363, 3441, 3531, 3621, 3723, 3759, 3783, 3813, 4011, 4029, 4071, 4161

Offset: 1

Author

M. F. Hasler, May 11 2009

Keywords

• nonn

Comments

This is in some sense the nontrivial part of A160350: Indeed, Kaplan (2007) has shown that Phi[pqr] has coefficients in {0,1,-1} if r = +-1 (mod pq), where pA160350 (i.e. of A117223) which do not satisfy this equality (i.e. which are not in A160353).

See A160350 for further details and references.

Examples

			a(1)=231=3*7*11 is the smallest "nontrivial" element of A160350 in the sense that it is neither of the form 2pq, and that its largest factor (11) is not congruent to +- 1 modulo the product of the smaller factors (3*7).
		

Links

• Robin Visser, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046389, A117223, A160350, A160353, A160354.

Programs

PARI

forstep( pqr=1,5999,2, my(f=factor(pqr)); #f~==3 & vecmax(f[,2])==1 & abs((f[3,1]+1)%(f[1,1]*f[2,1])-1)!=1 & vecmax(abs(Vec(polcyclo(pqr))))==1 & print1(pqr","))

Formula

Equals A117223 \ A160353 = A160354 intersect A046389.