A116905 Number of partitions of n-th 3-almost prime into 2 squares.

1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 1, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1

Offset

1,11

Comments

See also A000161 Number of partitions of n into 2 squares (when order does not matter and zero is allowed).

Links

Table of n, a(n) for n=1..57.

Formula

a(n) = A000161(A014612(n)).

Example

a(1) = 1 because A014612(1) = 8 = 2^2 + 2^2, the unique sum of squares.
a(2) = 0 because A014612(2) = 12 has no decomposition into sum of 2 squares because it has a prime factor p == 3 (mod 4) with an odd power.
a(11) = 2 because A014612(11) = 50 = 2*5^2 = 1^2 + 7^2 = 5^2 + 5^2.
a(30) = 2 because A014612(30) = 125 = 5^3 = 2^2 + 11^2 = 5^2 + 1^0.
a(31) = 2 because A014612(31) = 130 = 2*5*13 = 3^2 + 11^2 = 7^2 + 9^2.
a(39) = 2 because A014612(39) = 170 = 2*5*17 = 1^2 + 13^2 = 7^2 + 11^2.

Crossrefs

Cf. A000161, A014612.

Sequence in context: A065860 A363494 A010110 * A115079 A286562 A185644

Adjacent sequences: A116902 A116903 A116904 * A116906 A116907 A116908

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 15 2006

Status

approved