A276557 Number of partitions of prime(n)^2 into squares of primes.

1, 1, 2, 4, 17, 39, 191, 410, 1771, 13805, 26459, 170897, 556698, 988053, 3019206, 15074481, 70202708, 115639004, 498047289, 1281427052, 2039282754, 7981334946, 19374343049, 71015123687, 380553620426, 862797574415, 1292837481584, 2875949125749, 4270259833946, 9334145396729

Offset: 1

Author

Ilya Gutkovskiy, Jun 14 2017

Keywords

• nonn

Examples

			a(3) = 2 because third square of prime is 25 and we have [25], [9, 4, 4, 4, 4].
		

Links

• Index entries for sequences related to sums of squares
• Index entries for related partition-counting sequences

Crossrefs

Cf. A001248, A037444, A056768, A078137, A090677.

Programs

Mathematica

Table[SeriesCoefficient[Product[1/(1 - x^Prime[k]^2), {k, 1, n}], {x, 0, Prime[n]^2}], {n, 1, 30}]

Formula

a(n) = [x^(prime(n)^2)] Product_{k>=1} 1/(1 - x^(prime(k)^2)).

a(n) = A090677(A001248(n)).