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A300675
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Number of monic irreducible polynomials of degree n over GF(16) that have a given nonzero trace.
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3
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1, 8, 85, 1024, 13107, 174760, 2396745, 33554432, 477218560, 6871947672, 99955602525, 1466015503360, 21651921285435, 321685687669320, 4803839602524143, 72057594037927936, 1085102592571150095, 16397105843297320960, 248545604361560274405, 3777893186295716170752, 57567896172125197996605
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (1/(16*n)) * Sum_{odd d divides n} mu(d)*16^(n/d), where mu is the Möbius function A008683.
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MATHEMATICA
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a[n_] := DivisorSum[n, MoebiusMu[#] * 16^(n/#) &, OddQ[#] &] / (16*n); Array[a, 21] (* Amiram Eldar, Oct 04 2023 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, if (d%2, moebius(d)*16^(n/d)))/(16*n); \\ Michel Marcus, Mar 11 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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