

A002183


Number of divisors of nth highly composite number.
(Formerly M0546 N0196)


58



1, 2, 3, 4, 6, 8, 9, 10, 12, 16, 18, 20, 24, 30, 32, 36, 40, 48, 60, 64, 72, 80, 84, 90, 96, 100, 108, 120, 128, 144, 160, 168, 180, 192, 200, 216, 224, 240, 256, 288, 320, 336, 360, 384, 400, 432, 448, 480, 504, 512, 576, 600, 640, 672, 720, 768, 800, 864, 896
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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


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

a(n) = A000005(A002182(n)).
Also record values of differences A006218(p)A006218(p1). These record values occur for any p = A002182(q) where q>=2.  Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Jun 23 2007
a(A261100(n)) = A070319(n).  Antti Karttunen, Jun 06 2017


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]] (* JeanFrançois Alcover, Aug 13 2013 *)


PROG

(Haskell)
import Data.List (nub)
a002183 n = a002183_list !! (n1)
a002183_list = nub $ map (a000005 . a061799) [1..]
 Reinhard Zumkeller, Apr 01 2011


CROSSREFS

Cf. A000005, A002182, A002201, A006218, A061799, A070319, A243220, A261100.
Sequence in context: A227762 A303492 A188591 * A060306 A158614 A303434
Adjacent sequences: A002180 A002181 A002182 * A002184 A002185 A002186


KEYWORD

nonn,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Robert G. Wilson v, Jul 24 2002


STATUS

approved



