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A345763 a(n) is the smallest k such that A345699(k) = n.

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%I A345763 #23 Jul 02 2021 11:38:34
%S A345763 1,4,16,20,1369,68,10201,148,272,5476,29997529,340,351649,40804,21904,
%T A345763 596,674041,1360,1852321,21908,163216,119990116,2649731918665280089,
%U A345763 2020,2301289,1406596,6416,204020,166497457681,87632,38862996769,2980,34351321,2696164,13965169
%N A345763 a(n) is the smallest k such that A345699(k) = n.
%t A345763 A345699[1] = 1; A345699[p_, 1] := A345699[p - 1];
%t A345763 A345699[p_, s_] := A345699[p, s] = A345699[p] + A345699[s];
%t A345763 A345699[n_] :=  A345699[n] = Module[{aux = FactorInteger[n]},
%t A345763     Product[A345699[aux[[i, 1]], aux[[i, 2]]], {i, Length[aux]}]];
%t A345763 a[n_]=0;
%t A345763 Table[If[a[A345699[n]] == 0, a[ A345699[n]]= n], {n, 1, 10^8}]
%t A345763 Table[a[n],{n,1,10}]
%Y A345763 Cf. A345699.
%K A345763 nonn
%O A345763 1,2
%A A345763 _José María Grau Ribas_, Jun 26 2021
%E A345763 a(23) corrected by and more terms from _Jinyuan Wang_, Jul 02 2021