A229298 -id:A229298 - cp's OEIS frontend

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

Original entry on oeis.org

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

Offset: 1

José María Grau Ribas, Sep 20 2013

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.

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.

Cf. A228919, A229298, A191677.

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}]

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