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

1,1

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

Table of n, a(n) for n=1..23.

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

Crossrefs

Cf. A099426.

Cf. A099806, A099807, A099808, A099809.

Sequence in context: A145851 A182374 A034207 * A172751 A350755 A013764

Adjacent sequences: A098967 A098968 A098969 * A098971 A098972 A098973

Keyword

nonn

Author

Hugo Pfoertner, Oct 24 2004

Extensions

More terms from James R. Buddenhagen, Oct 26 2004

Status

approved