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%I #6 May 14 2021 02:54:05
%S 1,6,24,80,273,960,3336,11480,39648,136952,472416,1630164,5625480,
%T 19412736,66992016,231184800,797806152,2753187210,9501109380,
%U 32787848746
%N a(n) is the least k such that the average number of bi-unitary divisors of {1..k} is >= n.
%F Lim_{n->oo} a(n+1)/a(n) = exp(1/A) = 3.4509501567..., where A is A306071.
%e a(2) = 6 since the average number of bi-unitary divisors of {1..6} is A306069(6)/6 = 13/6 > 2.
%t f[p_, e_] := If[OddQ[e], e + 1, e]; bdivnum[1] = 1; bdivnum[n_] := Times @@ (f @@@ FactorInteger[n]); seq={}; s = 0; k = 1; Do[While[s = s + bdivnum[k]; s < k*n, k++]; AppendTo[seq, k]; k++, {n, 1, 10}]; seq
%Y Cf. A286324, A306069, A306071.
%Y The unitary version of A085829.
%Y Similar sequences: A328331, A336304, A338891, A338943, A344272, A344274.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, May 13 2021