|
Search: id:A129575
|
|
|
| A129575 |
|
Exponential abundant numbers: integers n for which A126164(n)>n, or equivalently for which A051377(n)>2n. |
|
+0
1
|
|
| 900, 1764, 3600, 4356, 4500, 4900, 6084, 6300, 7056, 8100, 8820, 9900, 10404, 11700, 12348, 12996, 14700, 15300, 17100, 19044, 19404, 20700, 21780, 22500, 22932, 25200, 26100, 27900, 29988, 30276, 30420, 30492, 31500, 33300, 33516, 34596
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
There are only 52189 exponential abundant numbers less than 50 million, which suggests that these account for approximately 0.1% of all integers.
|
|
REFERENCES
|
Hagis, Peter Jr.; Some Results Concerning Exponential Divisors, Internat. J. Math. & Math. Sci., Vol. 11, No. 2, (1988), pp. 343-350.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, e-Divisor.
|
|
EXAMPLE
|
The third integer that is exceeded by its proper exponential divisor sum is 3600. Hence a(3)=3600.
|
|
MATHEMATICA
|
ExponentialDivisors[1]={1}; ExponentialDivisors[n_]:=Module[{}, {pr, pows}=Transpose@FactorInteger[n]; divpowers=Distribute[Divisors[pows], List]; Sort[Times@@(pr^Transpose[divpowers])]]; properexponentialdivisorsum[k_]:=Plus@@ExponentialDivisors[k]-k; Select[Range[5 10^4], properexponentialdivisorsum[ # ]># &]
|
|
CROSSREFS
|
Cf. A126164, A051377, A049419, A054979, A054980.
Sequence in context: A061044 A127658 A137490 this_sequence A074853 A162143 A069096
Adjacent sequences: A129572 A129573 A129574 this_sequence A129576 A129577 A129578
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Ant King (mathstutoring(AT)ntlworld.com), Apr 28 2007
|
|
|
Search completed in 0.002 seconds
|
