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

1,3

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A000040, A001156.

Sequence in context: A231187 A055529 A337723 * A222735 A299408 A338937

Adjacent sequences: A379548 A379549 A379550 * A379552 A379553 A379554

Keyword

nonn,new

Author

David James Sycamore, Dec 25 2024

Extensions

More terms from Michael De Vlieger, Dec 26 2024.

Status

approved