A376074 a(n) is the number of distinct right circular cones with integer radius and height having the same volume as a sphere with radius n.

2, 3, 4, 5, 4, 6, 4, 6, 8, 6, 4, 10, 4, 6, 8, 8, 4, 12, 4, 10, 8, 6, 4, 12, 8, 6, 10, 10, 4, 12, 4, 9, 8, 6, 8, 20, 4, 6, 8, 12, 4, 12, 4, 10, 16, 6, 4, 16, 8, 12, 8, 10, 4, 15, 8, 12, 8, 6, 4, 20, 4, 6, 16, 11, 8, 12, 4, 10, 8, 12, 4, 24, 4, 6, 16, 10, 8, 12, 4

Offset: 1

Author

Felix Huber, Sep 20 2024

Keywords

• nonn

Comments

a(n) is also the number of solutions to x^2*y = 4*n^3 in positive integers x and y.

Examples

			a(3) = 4 counts the following right circular cones (r, h): (1, 108), (2, 27), (3, 12), (6, 3). These 4 cones have the same volume as a sphere with radius 3: (1/3)*Pi*1^2*108 = (1/3)*Pi*2^2*27 = (1/3)*Pi*3^2*12 = (1/3)*Pi*6^2*3 = (4/3)*Pi*3^3 = 36*Pi.
		

Links

• Felix Huber, Table of n, a(n) for n = 1..10000
• Felix Huber, Maple programs
• Eric Weisstein's World of Mathematics, Cone
• Eric Weisstein's World of Mathematics, Sphere

Crossrefs

Cf. A375576, A375580, A375785.

Programs

Maple

See Huber link.