A123048 Semiprimes that are the sum of a positive square and a positive cube.

9, 10, 26, 33, 57, 65, 82, 91, 122, 129, 134, 141, 145, 161, 177, 185, 206, 217, 226, 265, 289, 321, 362, 381, 407, 427, 485, 505, 511, 537, 566, 626, 633, 667, 681, 689, 703, 737, 745, 778, 785, 793, 841, 842, 849, 898, 901, 905, 985, 1018, 1041, 1057, 1081

Offset: 1

Author

Jonathan Vos Post, Sep 25 2006

Keywords

• easy
• nonn

Comments

Semiprime analog of A066649, Primes of the form a^2 + b^3 with a, b > 0.

Examples

			a(1) = 9 = 2^3 + 1^2 = 3*3.
a(2) = 10 = 3^2 + 1^3 = 2*5.
a(3) = 26 = 5^2 + 1^3 = 2*13.
a(4) = 33 = 5^2 + 2^3 = 3*11.
a(5) = 57 = 7^2 + 2^3 = 3*19.
a(6) = 65 = 1^2 + 4^3 = 8^2 + 1^3 = 5*13.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A055394, A066649.

Programs

Mathematica

Select[ Union[ Plus @@@ Tuples[{Range[4^3]^2, Range[4^2]^3}]], # < 1082 && Plus @@ Last /@ FactorInteger[#] == 2 &] (* Giovanni Resta, Jun 12 2016 *)

Formula

A001358 INTERSECTION A055394.

Extensions

More terms from Robert G. Wilson v, Sep 29 2006