Curvatures of spheres in one bowl of integers, the Loeschian spheres. Mod 12, numbers equal to 0, 1, 3, 4, 7, 9. - Ed Pegg Jr , Jan 10 2017

The number of structure units in an icosahedral virus is 20*a(n) for an integer n, see Stannard link. - Charles R Greathouse IV , Nov 03 2015

Lame's solutions to the Helmholtz equation with Dirichlet boundary conditions on the unit-edged equilateral triangle have eigenvalues of the form: (x^2+x*y+y^2)*(4*Pi/3)^2. The actual set, starting at 1 and counting degeneracies, is given by A060428 , e.g., the first degeneracy is 49 where (x,y)=(0,7) and (3,5). - Robert Stephen Jones , Oct 01 2015

Sequence of divisors of the hexagonal lattice, except zero (where it is said that an integer n divides a lattice if there exists a sublattice of index n; example: 3 divides the hexagonal lattice). - Jean-Christophe Hervé , May 01 2013

Numbers of the form (x^2 + y^2 + (x + y)^2)/2. If we let z = - x - y, then all the solutions to x^2 + y^2 + z^2 = k with x + y + z = 0 are k = 2a(n) for any n. - Jon Perry , Dec 16 2012

The number of coat proteins at each corner of a triangular face of a virus shell. - Parthasarathy Nambi , Sep 04 2007

Equivalently, numbers n such that the coefficient of x^n in a(x) (resp. b(x)) is nonzero where a(), b() are cubic AGM functions. - Michael Somos , Jan 16 2011

Equivalently, numbers n such that the coefficient of x^n in Theta3(x)*Theta3(x^3) is nonzero. - Joerg Arndt , Jan 16 2011

Theorem (Schering, Delone, Watson): The only positive definite binary quadratic forms that represent the same numbers are x^2+xy+y^2 and x^2+3y^2 (up to scaling). - N. J. A. Sloane , Jun 22 2014

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