A126167 Number of primitive exponential amicable pairs (i,j) with i<j and i<=10^n.

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

Offset

1,6

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.

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

Table of n, a(n) for n=1..11.

Pedersen J. M., Known exponential amicable pairs.

Example

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

Crossrefs

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

Sequence in context: A121368 A010073 A264763 * A026260 A371061 A169655

Adjacent sequences: A126164 A126165 A126166 * A126168 A126169 A126170

Keyword

hard,nonn

Author

Ant King, Dec 21 2006

Extensions

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

Status

approved