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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
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
1,1
COMMENTS
a(n) is also the number of solutions to x^2*y = 4*n^3 in positive integers x and y.
LINKS
Felix Huber, Maple programs
Eric Weisstein's World of Mathematics, Cone
Eric Weisstein's World of Mathematics, Sphere
EXAMPLE
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.
MAPLE
See Huber link.
CROSSREFS
KEYWORD
nonn
AUTHOR
Felix Huber, Sep 20 2024
STATUS
approved