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%I #12 Jun 13 2021 03:22:58
%S 3,54,458,3480,25867,191351,1414204,10450027,77216338
%N a(n) is the largest integer k such that A345073(k) = n.
%H David E. Radford, <a href="https://arxiv.org/abs/2106.02002">Factorials and powers, a minimality result</a>, arXiv:2106.02002 [math.NT], 2021.
%H David E. Radford, <a href="https://arxiv.org/abs/2106.02109">Factorials and powers, a minimality result, revisited</a>, arXiv:2106.02109 [math.NT], 2021. See p. 10.
%o (PARI) f(n) = my(k=1); while (exp(1)*sqrtn(n!, n) >= n+k, k++); k; \\ A345073
%o lista(nn) = {my(m=2, nm); for (n=2, nn, nm = f(n); if (nm > m, m = nm; print1(n-1, ", ")););}
%Y Cf. A001113 (e), A345073.
%K nonn,hard,more
%O 2,1
%A _Michel Marcus_, Jun 07 2021
%E Offset changed to 2 and a(8)-a(10) from _Jinyuan Wang_, Jun 13 2021
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