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A126167
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Number of primitive exponential amicable pairs (i,j) with i<j and i<=10^n.
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0
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0, 0, 0, 0, 1, 2, 3, 5, 8, 8, 12
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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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.
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REFERENCES
| Hagis, Peter Jr.; Some Results Concerning Exponential Divisors, International Journal of Mathematics and Mathematical Sciences, Vol. 11, No. 2, (1988), pp. 343-350.
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LINKS
| Pedersen J. M., Known exponential amicable pairs.
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EXAMPLE
| a(7)=3 because there are 3 primitive exponential pairs (m,n) with m<n and m<=10^7
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CROSSREFS
| Cf. A051377, A054979, A049419, A054980, A126164, A126165, A126166.
Sequence in context: A141804 A121368 A010073 * A026260 A002153 A047607
Adjacent sequences: A126164 A126165 A126166 * A126168 A126169 A126170
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KEYWORD
| hard,nonn
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AUTHOR
| Ant King (mathstutoring(AT)ntlworld.com), Dec 21 2006
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EXTENSIONS
| Link corrected and reference added by Andrew Lelechenko (andrew.lelechenko(AT)gmail.com), Dec 04 2011
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