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%I #17 Dec 30 2020 12:02:40
%S 1,0,5,18,164,1538,20018,408404,7759748,148728578,0,194482899488,0,
%T 286353189202064,0,491911826070793124,32087786808310197824,
%U 1809656800145141307344,113734187984879487014048,0,0,27153120399499349433747548978,0
%N a(n) is the smallest k such that usigma(k) = A002110(n), or 0 if no such k exists.
%e a(3) = 18 because usigma(18) = 30 = A002110(3) and 18 is the smallest number with this property.
%o (PARI) nthprimorial(n)=prod(i=1,n, prime(i));
%o usigma(n,f=factor(n))=prod(i=1,#f~, f[i,1]^f[i,2]+1);
%o a(n)=my(target=nthprimorial(n)); forfactored(n=target*nthprimorial(n-1)\usigma(nthprimorial(n-1)),target, if(usigma(n[1],n[2])==target, return(n[1]))); 0 \\ _Charles R Greathouse IV_, Aug 23 2017
%Y Cf. A002110, A034448, A289126.
%K nonn,more
%O 0,3
%A _Amiram Eldar_ and _Altug Alkan_, Aug 23 2017
%E a(10)-a(18) from _Giovanni Resta_, Aug 23 2017
%E a(19)-a(22) from _Daniel Suteu_, Dec 29 2020