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A036451
Maximal value of d(x) (the number of divisors of x, A000005) if the binary order (see A029837) of x, the value g(x) = n.
5
1, 2, 3, 4, 6, 8, 12, 16, 20, 24, 32, 40, 48, 64, 80, 96, 120, 144, 168, 200, 240, 288, 360, 432, 504, 600, 720, 864, 1008, 1152, 1344, 1600, 1920, 2304, 2688, 3072, 3584, 4096, 4800, 5760, 6720, 7680, 8640, 10080, 11520, 13824, 16128, 18432, 20736, 23040
OFFSET
0,2
COMMENTS
g(x) <= n can be replaced by g(x) = n.
LINKS
Giovanni Resta, Table of n, a(n) for n = 0..250 (based on A002182 b-file)
EXAMPLE
In the range of g(x) <= 5, the values of d(x) can be: 1, 2, 3, 4, 5, 6, 8 of which 8 is the maximal, so a(n) = a(g(x)) = 8.
MATHEMATICA
Max /@ Table[DivisorSigma[0, Floor[2^(n - 1) + k]], {n, 0, 22}, {k, Ceiling[2^(n - 1)]}] (* Michael De Vlieger, May 10 2017 *)
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(22)-a(32) from Alex Ratushnyak, Jun 06 2013
a(33)-a(49) from Giovanni Resta, Jun 06 2013
STATUS
approved