A228919 -id:A228919 - cp's OEIS frontend

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

Original entry on oeis.org

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

Offset: 1

José María Grau Ribas, Sep 20 2013

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

Compare with A229299(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. A191677, A228919, A229299.

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}]

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}]

A228926 Sum(m^(n+1), m=1...n-1) modulo n.

Original entry on oeis.org

0, 1, 2, 0, 0, 3, 0, 0, 6, 5, 0, 0, 0, 7, 7, 0, 0, 9, 0, 0, 14, 11, 0, 0, 0, 13, 18, 0, 0, 15, 0, 0, 22, 17, 23, 0, 0, 19, 26, 0, 0, 21, 0, 0, 30, 23, 0, 0, 0, 25, 34, 0, 0, 27, 44, 0, 38, 29, 0, 0, 0, 31, 42, 0, 0, 33, 0, 0, 46, 35, 0, 0, 0, 37, 35, 0, 66

Offset: 1

José María Grau Ribas, Sep 08 2013

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A121706, A228919, A204187.

f[n_] := Mod[Sum[PowerMod[i,n+1,n], {i, 1, n}], n]; Table[f[n], {n, 100}]

a(n)=lift(sum(m=1,n-1,Mod(m,n)^(n+1))) \\ Charles R Greathouse IV, Dec 27 2013

a(n) = A121706(n) mod (n-1). - T. D. Noe, Sep 16 2013

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A228926 Sum(m^(n+1), m=1...n-1) modulo n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula