

A208882


Number of representations of square of prime(n) as a^2 + b^2 + c^2 with 0 < a <= b <= c.


0



0, 1, 0, 1, 2, 1, 2, 3, 3, 3, 4, 4, 5, 6, 6, 6, 8, 7, 9, 9, 9, 10, 11, 11, 12, 12, 13, 14, 13, 14, 16, 17, 17, 18, 18, 19, 19, 21, 21, 21, 23, 22, 24, 24, 24, 25, 27, 28, 29, 28, 29, 30, 30, 32, 32, 33, 33, 34, 34, 35, 36, 36, 39, 39, 39, 39, 42, 42, 44, 43, 44
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OFFSET

1,5


COMMENTS

Almost monotonically increasing sequence, only rarely a(n)<=a(n1), contrary to case of n instead of p(n) (A181786).


LINKS

Table of n, a(n) for n=1..71.


EXAMPLE

a(2)=1 because p(2)=3 and 3^2=1^2+2^2+2^2,
a(4)=1 because p(4)=7 and 7^2=2^2+3^2+6^2,
a(5)=2 because p(5)=11 and 11^2=2^2+6^2+9^2=6^2+6^2+7^2.


MATHEMATICA

Table[Length[FindInstance[{Prime[n]^2==a^2+b^2+c^2, 0<a<=b<=c}, {a, b, c}, Integers, 100]], {n, 80}] (* Harvey P. Dale, Mar 06 2020 *)


CROSSREFS

Cf. A181786.
Sequence in context: A228285 A020908 A240873 * A186519 A241091 A137719
Adjacent sequences: A208879 A208880 A208881 * A208883 A208884 A208885


KEYWORD

nonn


AUTHOR

Zak Seidov, Mar 02 2012


STATUS

approved



