A217660 Numbers that give records for f(n)= (log(d(n))*log(log(n)))/(log(2)*log(n)) with d(n) the number of divisors.

2, 3, 4, 6, 8, 10, 12, 18, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 10080, 15120, 27720, 55440, 110880, 166320, 332640, 720720, 1441440, 2162160, 4324320, 21621600, 367567200, 6983776800

Offset

1,1

Comments

It is proved that the function f reaches its maximum for n = 6983776800, and that max n>=2 f(n) = 1.5379. The proof deals with superior highly composite numbers introduced by Ramanujan. So n = 6983776800 is the final term of this sequence.

Links

Table of n, a(n) for n=1..36.

J. L. Nicolas and G. Robin, Majorations explicites pour le nombre de diviseurs de N, Canad. Math. Bull. 26(1983), pp. 485-492.

Prog

(PARI) f(n) = {maxx = -999; for (i=2, n, x = (log(numdiv(i))*log(log(i)))/(log(2)*log(i)); if (x > maxx, maxx = x; print1(i, ", "); ); ); }

Crossrefs

Sequence in context: A245779 A120432 A020490 * A275581 A014875 A029469

Adjacent sequences: A217657 A217658 A217659 * A217661 A217662 A217663

Keyword

nonn,fini,full

Author

Michel Marcus, Nov 01 2012

Extensions

a(36) and keyword "full" added by Donovan Johnson, Nov 01 2012

Status

approved