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

1,1

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 p<q<r are primes. Here we list the odd elements of A160350 (i.e. of A117223) which do not satisfy this equality (i.e. which are not in A160353).

See A160350 for further details and references.

Links

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

Formula

Equals A117223 \ A160353 = A160354 intersect A046389.

Example

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).

Prog

(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", "))

Crossrefs

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

Sequence in context: A350367 A337231 A117223 * A211712 A324315 A276832

Adjacent sequences: A160352 A160353 A160354 * A160356 A160357 A160358

Keyword

nonn

Author

M. F. Hasler, May 11 2009

Status

approved