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

1,3

Links

Table of n, a(n) for n=1..30.

Index entries for sequences related to sums of squares

Index entries for related partition-counting sequences

Formula

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

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A081356 A018269 A270359 * A266868 A203177 A096122

Adjacent sequences: A276554 A276555 A276556 * A276558 A276559 A276560

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 14 2017

Status

approved