A355059 - OEIS

%I #11 Aug 06 2022 08:28:34

%S 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,

%T 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,

%U 6,7,6,6,9,6,7,9,8,7,6,8,8,6,6,11,8,8

%N 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).

%H Vladislav Shubin, <a href="/A355059/b355059.txt">Table of n, a(n) for n = 1..1000</a>

%t DedekindPsi[n_] := n * Product[(1 + 1/i), {i, FactorInteger[n][[All, 1]]}];

%t bound = 86

%t For[s = 1, s <= bound, s++,

%t    If[s == 1, Print["m   =   ", 1]; s = s + 1;];

%t    Q = Prime[s];

%t    InitialArray = FactorInteger[If[Q != 3, 3*(Q + 1), 2]];

%t    For[i = 1, i <= Length[InitialArray] - 1, i++,

%t         CurrentArray = FactorInteger[InitialArray[[-i, 1]] + 1] ~Join~ InitialArray;

%t         InitialArray = FactorInteger[Product[CurrentArray[[k, 1]] ^ CurrentArray[[k, 2]], {k, 1, Length[CurrentArray]}]];

%t    ];

%t         InitialArray = InitialArray~Join~{{Q, 0}};

%t         m = Max[InitialArray[[All, 2]]];

%t    If[Q == 3, m = m + 1];

%t    Print["m   =   ", m]

%t ];

%Y Cf. A001615, A007947, A355045.

%K nonn

%O 1,1

%A _Vladislav Shubin_, Jun 16 2022