A355059 a(n) is the positive integer such that psi(A355045(n)) = rad(A355045(n))^a(n), where psi(k) = A001615(k) and rad(k) = A007947(k).

2, 2, 3, 5, 4, 6, 3, 5, 5, 4, 7, 6, 6, 6, 6, 4, 5, 8, 5, 5, 7, 7, 7, 4, 6, 4, 9, 4, 6, 6, 9, 6, 6, 8, 4, 8, 8, 8, 8, 5, 5, 7, 8, 7, 5, 6, 5, 10, 7, 7, 7, 7, 5, 7, 7, 7, 5, 7, 9, 7, 7, 6, 9, 9, 9, 5, 9, 7, 6, 7, 6, 6, 9, 6, 7, 9, 8, 7, 6, 8, 8, 6, 6, 11, 8, 8

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, A355045.

Programs

Mathematica

DedekindPsi[n_] := n * Product[(1 + 1/i), {i, FactorInteger[n][[All, 1]]}];
bound = 86
For[s = 1, s <= bound, s++,
   If[s == 1, Print["m   =   ", 1]; s = s + 1;];
   Q = 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]]];
   If[Q == 3, m = m + 1];
   Print["m   =   ", m]
];