A098970 - OEIS

%I #14 May 08 2021 23:37:54

%S 19,67695,411292,1134035,1184876,2112836,2455255,4073384,11293009,

%T 16171470,18589912,34388501,63609329,63711615,117446600,166530856,

%U 284034387,449805631,637548135,685361103,783484793,888180400,1121365940

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

%C This sequence resulted from a discussion on the seqfan mailing list started by _Ed Pegg Jr_.

%C _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.

%C The numbers 12*k form a subsequence of A099426. - _Hans Havermann_, Oct 24 2004

%C 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

%H James Buddenhagen, <a href="http://www.buddenbooks.com/jb/num_theory/sum_of_2_cubes_a_square.htm">Two Primes Cubed which Sum to a Square</a>.

%Y Cf. A099426.

%Y Cf. A099806, A099807, A099808, A099809.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Oct 24 2004

%E More terms from _James R. Buddenhagen_, Oct 26 2004