A376074 - OEIS

%I #9 Oct 02 2024 14:35:49

%S 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,

%T 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,

%U 4,6,16,11,8,12,4,10,8,12,4,24,4,6,16,10,8,12,4

%N 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.

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

%H Felix Huber, <a href="/A376074/b376074.txt">Table of n, a(n) for n = 1..10000</a>

%H Felix Huber, <a href="/A376074/a376074.txt">Maple programs</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Cone.html">Cone</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Sphere.html">Sphere</a>

%e 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.

%p See Huber link.

%Y Cf. A375576, A375580, A375785.

%K nonn

%O 1,1

%A _Felix Huber_, Sep 20 2024