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

Author

M. F. Hasler, May 11 2009

Keywords

• nonn

Comments

Kaplan (2007) has shown that Phi(pqr) has coefficients in {0,1,-1} if r = +-1 (mod pq), where pA160350 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.

Examples

			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).
		

Links

• Robin Visser, Table of n, a(n) for n = 1..10000
• Nathan Kaplan, Flat cyclotomic polynomials of order three, J. Number Theory 127 (2007), 118-126.

Programs

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","))

Formula

Equals A160350 \ A160352.