

A160354


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


2



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
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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



FORMULA



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



KEYWORD

nonn


AUTHOR



STATUS

approved



