A045701 Number of ways n can be written as a sum of a square of a prime and a cube of a prime.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,129

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

Formula

G.f.: (Sum_{k>=1} x^(prime(k)^2))*(Sum_{k>=1} x^(prime(k)^3)). - Ilya Gutkovskiy, Jan 06 2017

Example

a(12) = 1 because 12 = 2^2 + 2^3; a(17) = 1 because 17 = 2^3 + 3^2.
a(129) = 2 because 129 = 2^3 + 11^2 = 2^2 + 5^3.

Crossrefs

Cf. A045699, A045700, A196752, A196753.

Sequence in context: A294937 A363131 A355447 * A277156 A353798 A193095

Adjacent sequences: A045698 A045699 A045700 * A045702 A045703 A045704

Keyword

easy,nonn

Author

Felice Russo

Extensions

More terms from Erich Friedman

Status

approved