The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A344274 a(n) is the least k such that the average number of infinitary divisors of {1..k} is >= n. 2
 1, 6, 24, 105, 385, 1554, 6063, 23688, 92610, 362112, 1416360, 5539296, 21663378, 84725487, 331362185, 1295952084, 5068450464, 19822658688 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS 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 * A122740 A034432 A026962 Adjacent sequences:  A344271 A344272 A344273 * A344275 A344276 A344277 KEYWORD nonn,more AUTHOR Amiram Eldar, May 13 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 20:25 EST 2021. Contains 349435 sequences. (Running on oeis4.)