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a(n) is the least k such that the average number of nonunitary divisors of {1..k} is >= n.
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%I #15 May 24 2021 01:32:10

%S 54,816,10530,135200,1733760,22216752,284685408,3647978320,

%T 46745561100,599002268832,7675674748560

%N a(n) is the least k such that the average number of nonunitary divisors of {1..k} is >= n.

%F Lim_{n->oo} a(n+1)/a(n) = exp(1/(1-1/zeta(2))) = exp(Pi^2/(Pi^2-6)) = 12.8140996101...

%e a(1) = 54 since the average of the number of nonunitary divisors of {1..54} is (Sum_{k=1..54} A056175(k))/54 = 1.

%t nd[n_] := DivisorSigma[0,n] - 2^PrimeNu[n]; seq={}; s = 0; k = 1; Do[While[s = s + nd[k]; s < k*n, k++]; AppendTo[seq, k]; k++, {n, 1, 5}]; seq

%Y Cf. A013661, A056175.

%Y The nonunitary version of A085829.

%Y Similar sequences: A328331, A336304, A338891, A338943, A344273, A344274.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, May 13 2021

%E a(10)-a(11) from _Martin Ehrenstein_, May 23 2021