OFFSET
1,2
COMMENTS
Invented by the HR (named after Hardy and Ramanujan) concept formation program.
Numbers in this sequence but not in A036455 are 1, 1260, 1440, 1800, 1980 etc. [From R. J. Mathar, Oct 20 2008]
tau(p^(n^2-1)) = n^2 so numbers of this form are in this sequence, and because tau is multiplicative: if a and b are in this sequence and (a,b)=1 then a*b is also in a(n). - Enrique Pérez Herrero, Jan 22 2013
What is the density of this sequence? It contains A030229 and thus has (lower) density at least 3/Pi^2 = 0.30396...; it does not contain any members of A030059 or A060687, and hence has (upper) density at most 1 - 3/Pi^2 - 6*A179119/Pi^2 = 0.49528.... - Charles R Greathouse IV, Jan 11 2025
REFERENCES
S. Colton, Automated Theorem Discovery: A Future Direction for Theorem Provers, 2002.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.
S. Colton, HR - Automatic Theory Formation in Pure Mathematics (Unfortunately [403 Forbidden])
S. Colton and A. Bundy, Automatic Concept Formation in Pure Mathematics
S. Colton, A. Bundy and T. Walsh, Agent Based Cooperative Theory Formation in Pure Mathematics
S. Colton, R. McCasland and A. Bundy, Automated Theory Formation for Tutoring Tasks in Pure Mathematics, 2002.
EXAMPLE
tau(6)=4, which is a square number, so 6 is in this sequence.
MATHEMATICA
Select[Range[200], IntegerQ[Sqrt[DivisorSigma[0, #]]]&] (* Harvey P. Dale, Apr 20 2011 *)
PROG
(PARI) is(n)=issquare(numdiv(n)) \\ Charles R Greathouse IV, Jan 22 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Simon Colton (simonco(AT)cs.york.ac.uk)
EXTENSIONS
Links corrected and edited by Daniel Forgues, Jun 30 2010
STATUS
approved