A056766 Smallest term of A056757 (numbers for which the cube of the number of divisors exceeds the number) between 2^(n-1) and 2^n.

2, 3, 5, 9, 18, 33, 66, 130, 258, 516, 1026, 2052, 4100, 8200, 16400, 32800, 65550, 131100, 262200, 524400, 1048800, 2097600, 4195200, 8390400, 16783200, 33566400, 67132800, 134265600, 268606800, 537213600, 1074427200, 2148854400, 4297708800, 8627018400, 18897278400

Offset: 1

Author

Labos Elemer, Aug 16 2000

Keywords

• nonn
• fini
• full

Comments

Smallest k so that 2^(n-1) < k <= 2^n and A000005(k)^3 > k.

Examples

			For n=7, 64 < a(7) = 66 < 128, A000005(66)^3 = 8^3 = 512 > 66, and no other such number occurs between 64 and 66.
For n=31, a(31) = 1074427200, 2^30 < a(31) < 2^31; a(31) has 1344 divisors and 1344^3 = 2427715584 > 1074427200. Between 2^30 and a(31) no other numbers occur with this property.
		

Crossrefs

Cf. A000005, A035033, A035034, A035035, A034884, A029837, A056757-A056767.

Extensions

a(33)-a(35) from Amiram Eldar, Aug 15 2024