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Let M(n) = maximal value of (n/k)^k over all k = 1, 2, ...; a(n) = ceiling(M(n)).
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%I #3 Mar 30 2012 16:50:49

%S 1,2,3,4,7,9,13,19,27,40,58,81,119,173,245,360,518,744,1086,1555,2255,

%T 3271,4668,6819,9847,14117,20590,29620,42763,62089,89056,129308,

%U 187065,267894,390500,563209,811021,1178089,1694775,2452060,3551314,5097656,7405862,10698506

%N Let M(n) = maximal value of (n/k)^k over all k = 1, 2, ...; a(n) = ceiling(M(n)).

%e The sequence of M(n)'s begins 1, 2, 3, 4, 6.2500000000000000000, 9, 12.703703703703703703..., 18.962962962962962963..., 27, 39.062500000000000000, 57.191406250000000000, 81, 118.81376000000000000, 172.10368000000000000, 244.14062500000000000, ...

%Y Suggested by A000792. Cf. A139050, A139051, A139076, A139077.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jun 03 2008