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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).

%I A355045 #17 Aug 06 2022 08:27:52
%S A355045 18,18,11250,57177414,8696754,10763393803185114,501126,23816977256250,
%T A355045 23981814018,230750426250,3730545397766934,33914855378546706844968750,
%U A355045 11135545745963323734,234030019748505421122,246218836545018,5018345916
%N 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).
%H A355045 Vladislav Shubin, <a href="/A355045/b355045.txt">Table of n, a(n) for n = 1..1000</a>
%t A355045 DedekindPsi[n_] :=
%t A355045   n * Product[(1 + 1/i), {i, FactorInteger[n][[All, 1]]}];
%t A355045 For[s = 2, s <= 49, s++,
%t A355045    If[s == 1, Print["n   =   ", 18]; s = s + 1;];
%t A355045    Q = 1*Prime[s];
%t A355045 InitialArray = FactorInteger[If[Q != 3, 3*(Q + 1), 2]];
%t A355045 For[i = 1, i <= Length[InitialArray] - 1, i++,
%t A355045   CurrentArray =
%t A355045    FactorInteger[InitialArray[[-i, 1]] + 1] ~Join~ InitialArray;
%t A355045       InitialArray =
%t A355045    FactorInteger[Product[CurrentArray[[k, 1]] ^ CurrentArray[[k, 2]], {k, 1,
%t A355045       Length[CurrentArray]}]];
%t A355045   ];
%t A355045 InitialArray = InitialArray ~Join~ {{Q, 0}};
%t A355045 m = Max[InitialArray[[All, 2]]];
%t A355045 n = Product[Power[InitialArray[[k, 1]], m - InitialArray[[k, 2]] + 1], {k, 1,
%t A355045     Length[InitialArray]}];
%t A355045 If[Q ==  3, m = m + 1];
%t A355045 Print["n   =   " n]];
%Y A355045 Cf. A001615, A007947.
%K A355045 nonn
%O A355045 1,1
%A A355045 _Vladislav Shubin_, Jun 16 2022