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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).

%I A355059 #11 Aug 06 2022 08:28:34
%S A355059 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 A355059 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 A355059 6,7,6,6,9,6,7,9,8,7,6,8,8,6,6,11,8,8
%N 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).
%H A355059 Vladislav Shubin, <a href="/A355059/b355059.txt">Table of n, a(n) for n = 1..1000</a>
%t A355059 DedekindPsi[n_] := n * Product[(1 + 1/i), {i, FactorInteger[n][[All, 1]]}];
%t A355059 bound = 86
%t A355059 For[s = 1, s <= bound, s++,
%t A355059    If[s == 1, Print["m   =   ", 1]; s = s + 1;];
%t A355059    Q = Prime[s];
%t A355059    InitialArray = FactorInteger[If[Q != 3, 3*(Q + 1), 2]];
%t A355059    For[i = 1, i <= Length[InitialArray] - 1, i++,
%t A355059         CurrentArray = FactorInteger[InitialArray[[-i, 1]] + 1] ~Join~ InitialArray;
%t A355059         InitialArray = FactorInteger[Product[CurrentArray[[k, 1]] ^ CurrentArray[[k, 2]], {k, 1, Length[CurrentArray]}]];
%t A355059    ];
%t A355059         InitialArray = InitialArray~Join~{{Q, 0}};
%t A355059         m = Max[InitialArray[[All, 2]]];
%t A355059    If[Q == 3, m = m + 1];
%t A355059    Print["m   =   ", m]
%t A355059 ];
%Y A355059 Cf. A001615, A007947, A355045.
%K A355059 nonn
%O A355059 1,1
%A A355059 _Vladislav Shubin_, Jun 16 2022