A045699 Numbers of the form p^2 + q^3, p,q prime.

12, 17, 31, 33, 36, 52, 57, 76, 129, 134, 148, 150, 174, 177, 196, 246, 294, 297, 316, 347, 352, 368, 369, 388, 392, 414, 464, 486, 512, 537, 556, 632, 654, 704, 849, 868, 872, 966, 969, 988, 1086, 1184, 1304, 1335, 1340, 1356, 1377, 1380, 1396, 1452

Offset: 1

Author

Felice Russo

Keywords

• nonn
• nice

Examples

			a(4)=36 because 36=3^3+3^2; a(7)=76 because 76=3^3+7^2.
		

Links

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

Crossrefs

Cf. A000040, A045700, A196752, A196753.

Programs

Mathematica

max = 1500; pp = Prime[Range[PrimePi[Sqrt[max]]]]; qq = Prime[Range[PrimePi[max^(1/3)]]]; Select[Union[Flatten[Outer[Plus, pp^2, qq^3]]], # <= max&] (* Jean-François Alcover, Apr 26 2011 *)
With[{upto=1500},Select[Union[Flatten[{#[[1]]^2+#[[2]]^3,#[[2]]^2+ #[[1]]^3}&/@ Tuples[Prime[Range[Floor[Sqrt[upto/8]]]],2]]],#<=upto&]] (* Harvey P. Dale, Dec 18 2018 *)

PARI

list(lim)=my(v=List(),t); lim\=1; forprime(q=2,sqrtnint(lim-4,3), t=q^3; forprime(p=2,sqrtint(lim-t), listput(v, p^2+t))); Set(v) \\ Charles R Greathouse IV, Jun 07 2016

Formula

Numbers n such that A045701(n)>0.