A379551 Number of partitions of prime(n) into squares.

1, 1, 2, 2, 4, 6, 9, 10, 14, 26, 28, 46, 60, 66, 84, 124, 169, 192, 256, 311, 347, 455, 545, 713, 993, 1167, 1255, 1466, 1590, 1846, 3042, 3491, 4279, 4564, 6312, 6712, 8094, 9697, 10923, 13027, 15460, 16368, 21585, 22795, 25392, 26778, 36651, 49641, 54801, 57560

Offset: 1

Author

David James Sycamore, Dec 25 2024

Keywords

• nonn

Examples

			prime(5) = 11 = 11*1^2 = 3^2+2*1^2 = 2*2^2+3*1^2 = 2^2+7*1^2, so a(5) = 4.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001156.

Programs

Mathematica

f[n_, i_] := f[n, i] = If[n == 0, 1, If[i < 1, 0, f[n, i - 1] + If[i^2 > n, 0, f[n - i^2, i] ] ] ]; Table[f[#, Floor@ Sqrt[#]] &[Prime[n]], {n, 120}] (* Michael De Vlieger, Dec 26 2024, after Jean-François Alcover at A001156 *)

Formula

a(n) = A001156(prime(n)).

Extensions

More terms from Michael De Vlieger, Dec 26 2024.