A229299 Number of terms in A191677 less than or equal to 10^n.

3, 30, 347, 3872, 41311, 430305, 4423115

Offset

1,1

Comments

0.50801 < lim A229299(n)/10^n = lim A229298(n)/10^n < 0.50966.

It seems that the convergence of A(n)/10^n is very slow; compare with A229298(n)/10^n.

Links

Table of n, a(n) for n=1..7.

J. M. Grau, A. M. Oller-Marcén, About the congruence sum_{k=1}^n k^f(n) == 0 (mod n), arXiv:1304.2678 [math.NT], 2013.

Mathematica

fa=FactorInteger; Carlitz[k_, n_] := Mod[n-Sum[If[IntegerQ[k/(fa[n][[i, 1]]-1)], n/fa[n][[i, 1]], 0], {i, 1, Length[fa[n]]}], n]; supercar[k_, n_] := If[k == 1 || Mod[k, 2] == 0 || Mod[n, 4] > 0, Carlitz[k, n], Mod[Carlitz[k, n] - n/2, n]]; Table[Print[Length@Select[Range[10^n], supercar[#-1, #] == 0 &]], {n, 1, 7}]

Crossrefs

Cf. A228919, A229298, A191677.

Sequence in context: A339626 A160473 A144283 * A365158 A178016 A365152

Adjacent sequences: A229296 A229297 A229298 * A229300 A229301 A229302

Keyword

nonn,more,hard

Author

José María Grau Ribas, Sep 20 2013

Status

approved