A078137 -id:A078137 - cp's OEIS frontend

A259241 Areas of rectangles that can be completely filled with squares of side length > 1 (with all side lengths restricted to the natural numbers).

4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 30, 32, 36, 40, 42, 44, 45, 48, 49, 50, 52, 54, 55, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 81, 84, 85, 88, 90, 91, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 115, 116, 117, 119, 120, 121, 124, 125

Offset: 1

Laurance L. Y. Lau, Jun 22 2015

nonn

Contains all integers from A013929.

Subset of A078137.

			See illustration in Links.

Giovanni Resta, Table of n, a(n) for n = 1..250
Giovanni Resta, Illustration of the first 48 squarefree terms

Cf. A078137.

a(14)-a(62) from Giovanni Resta, Jun 22 2015

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Jun 14 2017

nonn

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

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

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

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

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

cp's OEIS Frontend

A259241 Areas of rectangles that can be completely filled with squares of side length > 1 (with all side lengths restricted to the natural numbers).

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