A098970 Numbers k such that (12*k)^2 can be expressed as the sum of the cubes of two distinct primes.

19, 67695, 411292, 1134035, 1184876, 2112836, 2455255, 4073384, 11293009, 16171470, 18589912, 34388501, 63609329, 63711615, 117446600, 166530856, 284034387, 449805631, 637548135, 685361103, 783484793, 888180400, 1121365940

Offset: 1

Author

Hugo Pfoertner, Oct 24 2004

Keywords

• nonn

Comments

This sequence resulted from a discussion on the seqfan mailing list started by Ed Pegg Jr.

Dean Hickerson and Paul C. Leopardi have shown that if a and b are distinct primes with a^3 + b^3 = c^2, then c must be divisible by 12.

The numbers 12*k form a subsequence of A099426. - Hans Havermann, Oct 24 2004

All terms of this sequence are of the form M*N*(3*M^4+N^4)/2 for some pair M,N of relatively prime positive integers of opposite parity. For each n, A099806(n)^3 + A099807(n)^3 = (12*A098970(n))^2. - James R. Buddenhagen, Oct 26 2004

Links

• James Buddenhagen, Two Primes Cubed which Sum to a Square.

Crossrefs

Cf. A099426.

Cf. A099806, A099807, A099808, A099809.

Extensions

More terms from James R. Buddenhagen, Oct 26 2004