A355045 a(n) is the least positive integer k which is a multiple of prime(n) such that for some m >= 0, psi(k) = rad(k)^m, where psi(k) = A001615(k) and rad(k) = A007947(k).

18, 18, 11250, 57177414, 8696754, 10763393803185114, 501126, 23816977256250, 23981814018, 230750426250, 3730545397766934, 33914855378546706844968750, 11135545745963323734, 234030019748505421122, 246218836545018, 5018345916

Offset: 1

Author

Vladislav Shubin, Jun 16 2022

Keywords

• nonn

Links

• Vladislav Shubin, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001615, A007947.

Programs

Mathematica

DedekindPsi[n_] :=
  n * Product[(1 + 1/i), {i, FactorInteger[n][[All, 1]]}];
For[s = 2, s <= 49, s++,
   If[s == 1, Print["n   =   ", 18]; s = s + 1;];
   Q = 1*Prime[s];
InitialArray = FactorInteger[If[Q != 3, 3*(Q + 1), 2]];
For[i = 1, i <= Length[InitialArray] - 1, i++,
  CurrentArray =
   FactorInteger[InitialArray[[-i, 1]] + 1] ~Join~ InitialArray;
      InitialArray =
   FactorInteger[Product[CurrentArray[[k, 1]] ^ CurrentArray[[k, 2]], {k, 1,
      Length[CurrentArray]}]];
  ];
InitialArray = InitialArray ~Join~ {{Q, 0}};
m = Max[InitialArray[[All, 2]]];
n = Product[Power[InitialArray[[k, 1]], m - InitialArray[[k, 2]] + 1], {k, 1,
    Length[InitialArray]}];
If[Q ==  3, m = m + 1];
Print["n   =   " n]];