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A328331 a(n) is the least k such that the average number of unitary divisors of {1..k} is >= n.

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%I A328331 #12 Oct 22 2019 21:19:45
%S A328331 1,6,35,190,1015,5304,27417,142142,736782,3816852,19774690,102446730,
%T A328331 530743749,2749606626,14244797910
%N A328331 a(n) is the least k such that the average number of unitary divisors of {1..k} is >= n.
%C A328331 The unitary version of A085829.
%F A328331 Lim_{n->oo} a(n+1)/a(n) = exp(zeta(2)) = exp(Pi^2/6) = 5.180668... (since A064608(n) ~ n*log(n)/zeta(2)).
%e A328331 a(2) = 6 because the average number of unitary divisors of {1..6} is  A064608(6)/6 = 13/6 > 2.
%t A328331 seq={}; s = 0; k = 1; Do[While[s += 2^PrimeNu[k]; s < k*n, k++]; AppendTo[seq, k]; k++, {n, 1, 10}]; seq
%Y A328331 Cf. A013661, A034444, A064608, A085829.
%K A328331 nonn,more
%O A328331 1,2
%A A328331 _Amiram Eldar_, Oct 22 2019