

A098970


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


5



19, 67695, 411292, 1134035, 1184876, 2112836, 2455255, 4073384, 11293009, 16171470, 18589912, 34388501, 63609329, 63711615, 117446600, 166530856, 284034387, 449805631, 637548135, 685361103, 783484793, 888180400, 1121365940
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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 A013764 A078353
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



