login
A276557
Number of partitions of prime(n)^2 into squares of primes.
0
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 14 2017
STATUS
approved