OFFSET
1,2
COMMENTS
Record values of tau(n).
RECORDS transform of A000005.
All powers of 2 are present through 2^17. No power of 2 above that is present at least through 2^51. - Comment from Robert G. Wilson v, modified by Ray Chandler, Nov 10 2005
No power of 2 above 2^17 is contained in this sequence - see McRae link for proof. - Graeme McRae, Apr 27 2006
All numbers of the form 9*2^n are present for n=0 through n=30. - Richard Peterson, Sep 07 2024
REFERENCES
S. Ramanujan, Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962, p. 87.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
A. Flammenkamp, First 1200 highly composite numbers.
Graeme McRae, Highly Composite Numbers.
S. Ramanujan, Table of First 103 Highly Composite Numbers.
N. J. A. Sloane, Transforms.
Eric Weisstein's World of Mathematics, Highly Composite Number.
FORMULA
MATHEMATICA
Reap[ For[ record = 0; n = 1, n <= 10^9, n = If[n < 60, n+1, n+60], tau = DivisorSigma[0, n]; If[tau > record, record = tau; Print[tau]; Sow[tau]]]][[2, 1]] (* Jean-François Alcover, Aug 13 2013 *)
PROG
(Haskell)
import Data.List (nub)
a002183 n = a002183_list !! (n-1)
a002183_list = nub $ map (a000005 . a061799) [1..]
-- Reinhard Zumkeller, Apr 01 2011
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from Robert G. Wilson v, Jul 24 2002
STATUS
approved