A094713 Number of ways that prime(n) can be represented as a^2+b^2+c^2 with c >= b >= a > 0.

0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 2, 1, 0, 1, 2, 1, 1, 0, 1, 0, 2, 3, 1, 3, 0, 2, 1, 2, 0, 3, 2, 2, 3, 0, 1, 1, 0, 3, 3, 2, 0, 1, 2, 0, 2, 0, 3, 2, 3, 0, 3, 4, 4, 0, 5, 0, 1, 5, 2, 4, 2, 0, 2, 2, 2, 2, 3, 3, 4, 0, 0, 2, 2, 0, 5, 1, 5, 4, 5, 2, 0, 3, 0, 3, 5, 2, 7, 0, 4, 0, 0, 5, 2, 0, 7, 8, 3, 2, 2, 4, 5, 8, 3

Offset

1,13

Links

T. D. Noe, Table of n, a(n) for n=1..10000

Example

a(13) = 2 because prime(13) = 41 = 1+4+36 = 9+16+16.

Mathematica

lim=25; pLst=Table[0, {PrimePi[lim^2]}]; Do[n=a^2+b^2+c^2; If[n<lim^2 && PrimeQ[n], pLst[[PrimePi[n]]]++ ], {a, lim}, {b, a, Sqrt[lim^2-a^2]}, {c, b, Sqrt[lim^2-a^2-b^2]}; pLst
Table[Count[PowersRepresentations[Prime[n], 3, 2], _?(Min[#]>0&)], {n, 110}]  (* Harvey P. Dale, Feb 17 2011 *)

Crossrefs

Cf. A085317 (primes that are the sum of three positive squares), A094712 (primes that are not the sum of three positive squares), A094714 (least prime having exactly n representations as the sum of three positive squares).

Sequence in context: A194514 A324667 A258260 * A123517 A178948 A203827

Adjacent sequences: A094710 A094711 A094712 * A094714 A094715 A094716

Keyword

nonn

Author

T. D. Noe, May 21 2004

Status

approved