A126167 Number of primitive exponential amicable pairs (i,j) with i

0, 0, 0, 0, 1, 2, 3, 5, 8, 8, 12

Offset: 1

Author

Ant King, Dec 21 2006

Keywords

• hard
• nonn

Comments

There are infinitely many exponential amicable pairs, for multiplying an exponential amicable pair by a squarefree integer coprime to each of its members will generate another exponential amicable pair. Accordingly, we refer to pairs like (90972,100548) as primitive exponential amicable pairs and to pairs like (454860,502740) that can be obtained from them as nonprimitive. This sequence counts the primitive pairs only.

Examples

			a(7)=3 because there are 3 primitive exponential pairs (m,n) with m<n and m<=10^7
		

References

• Hagis, Peter Jr.; Some Results Concerning Exponential Divisors, International Journal of Mathematics and Mathematical Sciences, Vol. 11, No. 2, (1988), pp. 343-350.

Links

• Pedersen J. M., Known exponential amicable pairs.

Crossrefs

Cf. A051377, A054979, A049419, A054980, A126164, A126165, A126166.

Extensions

Link corrected and reference added by Andrew Lelechenko, Dec 04 2011