

A160355


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


3



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
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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



FORMULA



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



KEYWORD

nonn


AUTHOR



STATUS

approved



