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%I #22 Aug 24 2023 02:31:29
%S 5,15,55,205,829,3409,14569,63319,280319,1256567,5695487,26039187,
%T 119939427,555899247,2590404239,12127122989,57005914349,268933430849,
%U 1272801132329,6041172226049,28747703565329,137119782755669,655421041672109,3138947897124609
%N Number of monic irreducible polynomials over GF(5) of degree <= n.
%H Alois P. Heinz, <a href="/A114947/b114947.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) ~ 5^(n+1) / (4*n). - _Vaclav Kotesovec_, Sep 05 2014
%p with(numtheory):
%p b:= n-> add(mobius(d) *5^(n/d)/n, d=divisors(n)):
%p a:= n-> add(b(k), k=1..n):
%p seq(a(n), n=1..30); # _Alois P. Heinz_, Sep 23 2008
%t f[n_] := DivisorSum[n, MoebiusMu[#] * 5^(n/#) &] / n; Accumulate[Array[f, 30]] (* _Amiram Eldar_, Aug 24 2023 *)
%o (PARI) a(n)=sum(m=1, n, 1/m* sumdiv(m, d, moebius(d)*5^(m/d) ) ); /* _Joerg Arndt_, Jul 04 2011 */
%Y Partial sums of A001692. 5th column of A143328. - _Alois P. Heinz_, Sep 23 2008
%K nonn
%O 1,1
%A Gary L Mullen (mullen(AT)math.psu.edu) and Ken Hicks, Jan 06 2006
%E More terms from _Alois P. Heinz_, Sep 23 2008
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