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A160355 Odd indices pqr of flat cyclotomic polynomials of order 3 which are not of the form r = +/-1 (mod pq). 3

%I #12 Aug 02 2023 09:59:57

%S 231,399,483,651,663,741,1113,1173,1209,1281,1311,1353,1443,1479,1533,

%T 1581,1599,1653,1833,1947,2163,2247,2301,2337,2379,2409,2829,2877,

%U 2915,3129,3297,3363,3441,3531,3621,3723,3759,3783,3813,4011,4029,4071,4161

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

%C 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).

%C See A160350 for further details and references.

%H Robin Visser, <a href="/A160355/b160355.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals A117223 \ A160353 = A160354 intersect A046389.

%e 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).

%o (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","))

%Y Cf. A046389, A117223, A160350, A160353, A160354.

%K nonn

%O 1,1

%A _M. F. Hasler_, May 11 2009

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Last modified February 23 04:31 EST 2024. Contains 370267 sequences. (Running on oeis4.)