A344274 a(n) is the least k such that the average number of infinitary divisors of {1..k} is >= n.

1, 6, 24, 105, 385, 1554, 6063, 23688, 92610, 362112, 1416360, 5539296, 21663378, 84725487, 331362185, 1295952084, 5068450464, 19822658688

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Formula

Lim_{n->oo} a(n+1)/a(n) = exp(1/(2*c)) = 3.9109891037..., where c is A327576.

Example

a(2) = 6 since the average number of infinitary divisors of {1..6} is A327573(6)/6 = 13/6 > 2.

Mathematica

f[p_, e_] := 2^DigitCount[e, 2, 1]; idivnum[1] = 1; idivnum[n_] := Times @@ (f @@@ FactorInteger[n]); seq={}; s = 0; k = 1; Do[While[s = s + idivnum[k]; s < k*n, k++]; AppendTo[seq, k]; k++, {n, 1, 10}]; seq

Crossrefs

Cf. A037445, A327573, A327576.

The infinitary version of A085829.

Similar sequences: A328331, A336304, A338891, A338943, A344272, A344273.

Sequence in context: A089378 A074414 A165793 * A372225 A122740 A034432

Adjacent sequences: A344271 A344272 A344273 * A344275 A344276 A344277

Keyword

nonn,more

Author

Amiram Eldar, May 13 2021

Status

approved