A160354 Indices pqr of flat cyclotomic polynomials of order 3 which are not of the form r = +/-1 (mod pq).

70, 130, 154, 170, 230, 231, 238, 266, 286, 322, 370, 374, 399, 418, 430, 434, 442, 470, 483, 494, 518, 530, 598, 638, 646, 651, 658, 663, 670, 682, 730, 741, 742, 754, 782, 806, 814, 826, 830, 854, 874, 902, 938, 962, 970, 986, 1022, 1030, 1034, 1054, 1066

Offset

1,1

Comments

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 elements of A160350 which do not satisfy this equality.

Yet most elements are even, i.e. in A075819. Sequence A160355 is the subsequence of odd terms. See A160350 for more details.

Links

Table of n, a(n) for n=1..51.

Nathan Kaplan, Flat cyclotomic polynomials of order three, J. Number Theory 127 (2007), 118-126.

Formula

Equals A160350 \ A160352.

Example

a(1)=70=2*5*7 is the smallest element of A160350 for which the largest factor (7) is not congruent to +- 1 modulo the product of the smaller factors (2*5).

Prog

(PARI) for( pqr=1, 1999, 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

Sequence in context: A024756 A254367 A113928 * A215111 A255801 A044193

Adjacent sequences: A160351 A160352 A160353 * A160355 A160356 A160357

Keyword

nonn

Author

M. F. Hasler, May 11 2009

Status

approved