A056767 Largest number of binary size n (i.e., between (n-1)-th and n-th powers of 2) with the following property: cube of its number of divisors is larger than the number itself.

2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2046, 4095, 8190, 16380, 32760, 65520, 131040, 262080, 524160, 1048320, 2097144, 4193280, 8386560, 16773900, 33547800, 67095600, 134191200, 268382400, 536215680, 1073709000, 2144142000, 4288284000

Offset

1,1

Links

Table of n, a(n) for n=1..32.

Formula

Largest terms of A056757 between 2^(n-1) and 2^n.

Example

These maximal terms are usually "near" to 2^n. For n=1..10 they are equal to 2^n. At n=21, a(21)=2097144, 1048576 < a(21) < 2097144 = 8*27*7*19*73 has d=128 divisors, of which the cube is d^3d=2097152. So this maximum is near to but still less than d^3.

Mathematica

Table[Last@ Select[Range @@ (2^{n - 1, n}), DivisorSigma[0, #]^3 > # &], {n, 22}] (* Michael De Vlieger, Dec 31 2016 *)

Prog

(PARI) a(n) = {k = 2^n; while(numdiv(k)^3 <= k, k--); k; } \\ Michel Marcus, Dec 11 2013

Crossrefs

Cf. A000005, A029837, A035033-A035035, A034884, A056757-A056767, A056781.

Sequence in context: A330127 A292568 A354600 * A008863 A145117 A172320

Adjacent sequences: A056764 A056765 A056766 * A056768 A056769 A056770

Keyword

fini,nonn

Author

Labos Elemer, Aug 16 2000

Extensions

a(32) from Michel Marcus, Dec 11 2013

Status

approved