A171606 Numbers expressible as A*B^A in two or more different ways, with A, B > 1.

648, 2048, 4608, 5184, 41472, 52488, 472392, 500000, 524288, 2654208, 3125000, 4718592, 10125000, 13436928, 21233664, 30233088, 46118408, 76236552, 134217728, 169869312, 344373768, 402653184, 512000000, 648000000, 737894528, 800000000, 838860800, 922640625

Offset: 1

Author

Robert Munafo, Dec 12 2009

Keywords

• nonn

Comments

For any relatively prime pair A and C, there are infinitely many solutions A*B^A=C*D^C, with B and D of the form B=C^W*A^X, D=C^Y*A^Z, and W,Y constrained by AW=CY+1 and X,Z constrained by CZ=AX+1. Details and examples on Munafo web page.

Examples

			648 = 3 * 6^3 = 2 * 18^2.
5184 = 4 * 6^4 = 3 * 12^3.
344373768 = 8 * 9^8 = 3 * 486^3 = 2 * 13122^2.
922640625 = 5 * 45^5 = 3 * 675^3.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• R. Munafo, Generalized Cullen and Woodall Numbers

Crossrefs

Cf. A171607, A235368.

Extensions

a(26)-a(28) from Giovanni Resta, Jul 12 2018