The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”). Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A070319 Max( tau(k) : k=1,2,3,...,n ) where tau(n)=A000005(n) is the number of divisors of x. 8
 1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Is this the same as A068509? - David Scambler, Sep 10 2012 They are different even asymptotically: A068509(n)=O(sqrt(n)), while a(n) does not have polynomial growth. One example where the sequences differ: a(625) = 24 < A068509(625). (The inequality is implied by the set {1,2,..,25} where each pair of the elements has lcm <= 625.) - Max Alekseyev, Sep 11 2012 The two sequences first differ when n = 336, due to the set of 21 elements {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 21, 24, 30, 36, 42, 48} where each pair of elements has lcm <= 336, while no positive integer <= 336 has more than 20 divisors. Therefore A068509(336) = 21 and A070319(336) = 20. - William Rex Marshall, Sep 11 2012 REFERENCES Sándor, J., Crstici, B., Mitrinović, Dragoslav S. Handbook of Number Theory I. Dordrecht: Kluwer Academic, 2006, p. 44. S. Wigert. Sur l’ordre de grandeur du nombre des diviseurs d’un entier. Arkiv. for Math. 3 (1907), 1-9. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 S. Ramanujan, Highly composite numbers, Proceedings of the London Mathematical Society, 2, XIV, 1915, 347 - 409. FORMULA a(n) = exp(log(2) log(n) / log(log(n)) + O(log(n) log(log(log(n))) / (log(log(n)))^2)). (See Sándor reference for more formulas.) - Eric M. Schmidt, Jun 30 2013 a(n) = A002183(A261100(n)). - Antti Karttunen, Jun 06 2017 MATHEMATICA a = {0}; Do[AppendTo[a, Max[DivisorSigma[0, n], a[[n]]]], {n, 120}]; Rest@ a (* Michael De Vlieger, Sep 29 2015 *) PROG (PARI) a(n)=vecmax(vector(n, k, numdiv(k))) (PARI) v=vector(100); v=1; for(n=2, #v, v[n]=max(v[n-1], numdiv(n))); v \\ Charles R Greathouse IV, Sep 12 2012 (Haskell) a070319 n = a070319_list !! (n-1) a070319_list = scanl1 max \$ map a000005 [1..] -- Reinhard Zumkeller, Apr 01 2011 (PARI) A070319(n, m=1, s=2)={for(k=s, n, m

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 4 15:36 EST 2021. Contains 349526 sequences. (Running on oeis4.)