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A058820 a(0) = 1, a(1) = 5; for n >= 2 a(n) is the number of degree-n monic reducible polynomials over GF(5), i.e., a(n) = 5^n - A001692(n).

%I A058820 #14 Aug 13 2023 02:48:02
%S A058820 1,5,15,85,475,2501,13045,66965,341875,1736125,8789377,44389205,
%T A058820 223796925,1126802885,5667555805,28483073133,143051171875,
%U A058820 718060661765,3602769749125,18069618626645,90599060546905,454130626863845,2275813711825285,11402627696161685,57121117919938125
%N A058820 a(0) = 1, a(1) = 5; for n >= 2 a(n) is the number of degree-n monic reducible polynomials over GF(5), i.e., a(n) = 5^n - A001692(n).
%C A058820 Dimensions of homogeneous subspaces of shuffle algebra over 5-letter alphabet (see A058766 for 2-letter case).
%D A058820 M. Lothaire, Combinatorics on words, Cambridge mathematical library, 1983, p. 126 (definition of shuffle algebra).
%t A058820 a[n_] := 5^n - DivisorSum[n, MoebiusMu[n/#] * 5^# &] / n; a[0] = 1; a[1] = 5; Array[a, 25, 0] (* _Amiram Eldar_, Aug 13 2023 *)
%o A058820 (PARI) a(n) = if (n<=1, 5^n, 5^n - sumdiv(n, d, moebius(d)*5^(n/d))/n); \\ _Michel Marcus_, Oct 30 2017
%Y A058820 Cf. A000351, A001692, A058766.
%K A058820 nonn
%O A058820 0,2
%A A058820 Claude Lenormand (claude.lenormand(AT)free.fr), Jan 04 2001
%E A058820 Better description from Sharon Sela (sharonsela(AT)hotmail.com), Feb 19 2002
%E A058820 More terms from _Michel Marcus_, Oct 30 2017