A344272 a(n) is the least k such that the average number of nonunitary divisors of {1..k} is >= n.

54, 816, 10530, 135200, 1733760, 22216752, 284685408, 3647978320, 46745561100, 599002268832, 7675674748560

Offset: 1

Author

Amiram Eldar, May 13 2021

Keywords

• nonn
• more

Examples

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

Crossrefs

Cf. A013661, A056175.

The nonunitary version of A085829.

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

Programs

Mathematica

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

Formula

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

Extensions

a(10)-a(11) from Martin Ehrenstein, May 23 2021