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A300675 Number of monic irreducible polynomials of degree n over GF(16) that have a given nonzero trace. 2
1, 8, 85, 1024, 13107, 174760, 2396745, 33554432, 477218560, 6871947672, 99955602525, 1466015503360, 21651921285435, 321685687669320, 4803839602524143, 72057594037927936, 1085102592571150095, 16397105843297320960, 248545604361560274405, 3777893186295716170752, 57567896172125197996605 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..500

F. Ruskey, C.R. Miers, J. Sawada, The number of irreducible polynomials and Lyndon words with given trace, SIAM J. Discrete Math. 14 (2001) 240-245.

FORMULA

a(n) = (1/(16*n)) * Sum_{odd d divides n} mu(d)*16^(n/d), where mu is the Möbius function A008683.

PROG

(PARI) a(n) = sumdiv(n, d, if (d%2, moebius(d)*16^(n/d)))/(16*n); \\ Michel Marcus, Mar 11 2018

CROSSREFS

Cf. A000048, A054660, A300674.

Sequence in context: A299176 A093103 A288691 * A241323 A349334 A261501

Adjacent sequences: A300672 A300673 A300674 * A300676 A300677 A300678

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 11 2018

STATUS

approved

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Last modified December 1 16:09 EST 2022. Contains 358468 sequences. (Running on oeis4.)