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

1, 6, 35, 190, 1015, 5304, 27417, 142142, 736782, 3816852, 19774690, 102446730, 530743749, 2749606626, 14244797910

Offset

1,2

Comments

The unitary version of A085829.

Links

Table of n, a(n) for n=1..15.

Formula

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)).

Example

a(2) = 6 because the average number of unitary divisors of {1..6} is  A064608(6)/6 = 13/6 > 2.

Mathematica

seq={}; s = 0; k = 1; Do[While[s += 2^PrimeNu[k]; s < k*n, k++]; AppendTo[seq, k]; k++, {n, 1, 10}]; seq

Crossrefs

Cf. A013661, A034444, A064608, A085829.

Sequence in context: A137628 A254826 A274373 * A346318 A009572 A027202

Adjacent sequences: A328328 A328329 A328330 * A328332 A328333 A328334

Keyword

nonn,more

Author

Amiram Eldar, Oct 22 2019

Status

approved