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Search: id:A077599
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| A077599 |
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Sequence of n such that -1 is a "double" root for M(n,x) (i.e. M(n,x)=(x+1)^2*Q(n,x)). |
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+0
7
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| 8, 9, 24, 45, 100, 117, 120, 125, 135, 171, 175, 180, 184, 224, 243, 248, 256, 261, 270, 304, 312, 324, 342, 343, 344, 360, 369, 405, 459, 468, 472, 475, 477, 486, 507, 513, 520, 531, 536, 578, 584, 603, 608, 625, 639, 640, 657, 664, 675, 704, 711, 720, 728
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The n-th Moebius polynomial M(n,x) satisfies M(n,-1)=mu(n), the Moebius function of n; thus -1 is a simple root of M(n,x) if n is not square-free. Hence these values could be called "double non-square-free numbers".
The n-th polynomial is divisible by (x+1)^3 for n=175, 343, 513, 800, 875. - T. D. Noe (noe(AT)sspectra.com), Jan 09 2008
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MATHEMATICA
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a[n_, 1]=1; a[n_, k_]:=a[n, k]=Sum[Floor[n/m] a[m, k-1], {m, n-1}]; t={}; Do[p=Table[a[n, k], {k, n}].(x^Range[0, n-1]); If[PolynomialMod[p, (x+1)^2]==0, AppendTo[t, n]], {n, 100}]; t - T. D. Noe (noe(AT)sspectra.com), Jan 09 2008
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CROSSREFS
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Cf. A074586, A074587, A077596, A077597, A077598, A077600, A077601.
Sequence in context: A074344 A081351 A032462 this_sequence A109097 A115645 A068435
Adjacent sequences: A077596 A077597 A077598 this_sequence A077600 A077601 A077602
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr) and Paul D. Hanna (pauldhanna(AT)juno.com), Nov 10 2002
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Jan 09 2008
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