This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A009287 #53 Aug 17 2025 02:52:03
%S A009287 3,4,6,12,60,5040,293318625600,
%T A009287 670059168204585168371476438927421112933837297640990904154667968000000000000
%N A009287 a(1) = 3; thereafter a(n+1) = least k with a(n) divisors.
%C A009287 The sequence must start with 3, since a(1)=1 or a(1)=2 would lead to a constant sequence. - _M. F. Hasler_, Sep 02 2008
%C A009287 The calculation of a(7) and a(8) is based upon the method in A037019 (which, apparently, is the method previously used by the authors of A009287). So a(7) and a(8) are correct unless n=a(6)=5040 or n=a(7)=293318625600 are "exceptional" as described in A037019. - _Rick L. Shepherd_, Aug 17 2006
%C A009287 a(7) is correct because 5040 is not exceptional (see A072066). - _T. D. Noe_, Sep 02 2008
%C A009287 Terms from a(2) to a(7) are highly composite (that is, found in A002182), but a(8) is not. - _Ivan Neretin_, Mar 28 2015 [Equivalently, the first 6 terms are in A002183, but a(7) is not. Note that the smallest number with at least a(7) divisors is A002182(695) ~ 1.77 * 10^59 with 293534171136 divisors, which is much smaller than a(8) ~ 6.70 * 10^75. - _Jianing Song_, Jul 15 2021]
%C A009287 Grime reported that Ramanujan unfortunately missed a(7) with 5040 divisors. - _Frank Ellermann_, Mar 12 2020
%C A009287 It is possible to prepend 2 to this sequence as follows. a(0) = 2; for n > 0, a(n) = the smallest natural number greater than a(n-1) with a(n-1) divisors. - _Hal M. Switkay_, Jul 03 2022
%D A009287 Amarnath Murthy, Pouring a few more drops in the ocean of Smarandache Sequences and Conjectures (to be published in the Smarandache Notions Journal) [Note: this author submitted two erroneous versions of this sequence to the OEIS, A036460 and A061080, entries which contained invalid conjectures.]
%H A009287 Jason Earls, <a href="https://pdfs.semanticscholar.org/4559/ac50797ddeda688576630c4d92229440a0a3.pdf#page=274">A note on the Smarandache divisors of divisors sequence and two similar sequences</a>, in Smarandache Notions Journal (2004), Vol. 14.1, page 274.
%H A009287 James Grime and Brady Haran, <a href="https://www.youtube.com/watch?v=PF2GtiApF3E">Infinite Anti-Primes</a>, Numberphile video (2016).
%F A009287 a(n) = A005179(a(n-1)).
%e A009287 5040 is the smallest number with 60 divisors.
%t A009287 f[n_] := Block[{k = 3, s = (Times @@ (Prime[Range[Length@ #]]^Reverse[# - 1])) & @ Flatten[FactorInteger[#] /. {a_Integer, b_} :> Table[a, {b}]] & /@ Range@ 10000}, Reap@ Do[Sow[k = s[[k]]], {n}] // Flatten // Rest]; f@ 6 (* _Michael De Vlieger_, Mar 28 2015, after _Wouter Meeussen_ at A037019 *)
%Y A009287 Coincides with A251483 for 1 <= n <= 7 (only).
%Y A009287 Cf. A000005, A005179, A037019, A251483.
%K A009287 nonn
%O A009287 1,1
%A A009287 _David W. Wilson_ and James Kilfiger (jamesk(AT)maths.warwick.ac.uk)
%E A009287 Entry revised by _N. J. A. Sloane_, Aug 25 2006