

A009287


a(1) = 3; thereafter a(n+1) = least k with a(n) divisors.


8




OFFSET

1,1


COMMENTS

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
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
a(7) is correct because 5040 not exceptional (see A072066).  T. D. Noe, Sep 02 2008
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
Grime reported that Ramanujan unfortunately missed a(7) with 5040 divisors.  Frank Ellermann, Mar 12 2020


REFERENCES

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, A036480 and A061080, entries which contained invalid conjectures.]


LINKS

Table of n, a(n) for n=1..8.
James Grime and Brady Haran, Infinite AntiPrimes, Numberphile video (2016).
Jason Earls, A note on the Smarandache divisors of divisors sequence and two similar sequences, in Smarandache Notions Journal (2004), Vol. 14.1, page 274.


FORMULA

a(n) = A005179(a(n1)).


EXAMPLE

5040 is the smallest number with 60 divisors.


PROG

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 *)


CROSSREFS

Cf. A000005, A005179, A037019.
Sequence in context: A202855 A182857 A251483 * A061080 A254049 A280289
Adjacent sequences: A009284 A009285 A009286 * A009288 A009289 A009290


KEYWORD

nonn


AUTHOR

David W. Wilson and James Kilfiger (jamesk(AT)maths.warwick.ac.uk)


EXTENSIONS

Entry revised by N. J. A. Sloane, Aug 25 2006


STATUS

approved



