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Search: id:A160354
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| A160354 |
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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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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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.
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REFERENCES
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Nathan Kaplan, Flat cyclotomic polynomials of order three, Journal of Number Theory 127 (2007) 118-126 (doi:10.1016/j.jnt.2007.01.008).
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FORMULA
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A160354 = A160350 \ A160352.
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EXAMPLE
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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).
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PROGRAM
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(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", "))
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CROSSREFS
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Sequence in context: A024748 A024756 A113928 this_sequence A044193 A044574 A043482
Adjacent sequences: A160351 A160352 A160353 this_sequence A160355 A160356 A160357
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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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