

A056767


Largest number of binary size n (i.e., between (n1)th and nth powers of 2) with the following property: cube of its number of divisors is larger than the number itself.


7



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
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OFFSET

1,1


LINKS

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


FORMULA

Largest terms of A056757 between 2^(n1) 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, A035033A035035, A034884, A056757A056767, A056781.
Sequence in context: A113010 A330127 A292568 * 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



