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A160354 Indices pqr of flat cyclotomic polynomials of order 3 which are not of the form r = +/-1 (mod pq). 3
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, May 11 2009
STATUS
approved

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Last modified April 22 15:04 EDT 2024. Contains 371905 sequences. (Running on oeis4.)