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 A345073 a(n) is the least integer k such that e * (n!)^(1/n) < n + k. 2
 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Jinyuan Wang, Table of n, a(n) for n = 1..1000 David E. Radford, Factorials and powers, a minimality result, arXiv:2106.02002 [math.NT], 2021. David E. Radford, Factorials and powers, a minimality result, revisited, arXiv:2106.02109 [math.NT], 2021. PROG (PARI) a(n) = my(k=1); while (exp(1)*sqrtn(n!, n) >= n+k, k++); k; CROSSREFS Cf. A001113 (e), A345074. Sequence in context: A230516 A192688 A156752 * A086673 A101787 A343607 Adjacent sequences:  A345070 A345071 A345072 * A345074 A345075 A345076 KEYWORD nonn AUTHOR Michel Marcus, Jun 07 2021 STATUS approved

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Last modified December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)