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Search: id:A160355
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| A160355 |
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Odd indices pqr of flat cyclotomic polynomials of order 3 which are not of the form r = +/-1 (mod pq). |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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FORMULA
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A160355 = A117223 \ A160353 = A160354 intersect A046389.
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EXAMPLE
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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).
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PROGRAM
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(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", "))
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CROSSREFS
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Sequence in context: A088289 A046009 A117223 this_sequence A029569 A152102 A152500
Adjacent sequences: A160352 A160353 A160354 this_sequence A160356 A160357 A160358
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), May 11 2009
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