A344273 a(n) is the least k such that the average number of bi-unitary divisors of {1..k} is >= n.

1, 6, 24, 80, 273, 960, 3336, 11480, 39648, 136952, 472416, 1630164, 5625480, 19412736, 66992016, 231184800, 797806152, 2753187210, 9501109380, 32787848746

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Formula

Lim_{n->oo} a(n+1)/a(n) = exp(1/A) = 3.4509501567..., where A is A306071.

Example

a(2) = 6 since the average number of bi-unitary divisors of {1..6} is A306069(6)/6 = 13/6 > 2.

Mathematica

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

Crossrefs

Cf. A286324, A306069, A306071.

The unitary version of A085829.

Similar sequences: A328331, A336304, A338891, A338943, A344272, A344274.

Sequence in context: A201189 A001788 A068711 * A320856 A047790 A133474

Adjacent sequences: A344270 A344271 A344272 * A344274 A344275 A344276

Keyword

nonn,more

Author

Amiram Eldar, May 13 2021

Status

approved