A229298 Number of terms in A228919 less than or equal to 10^n.

5, 54, 515, 5109, 50933, 508932, 5087994

Offset: 1

Author

José María Grau Ribas, Sep 20 2013

Keywords

• nonn
• more
• hard

Comments

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

Compare with A229299(n)/10^n.

Links

• 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.

Crossrefs

Cf. A191677, A228919, A229299.

Programs

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}]