|
Search: id:A114286
|
|
|
| A114286 |
|
Sum of the cubes of the first n cubefree numbers. |
|
+0
2
|
|
| 0, 1, 9, 36, 100, 225, 441, 784, 1513, 2513, 3844, 5572, 7769, 10513, 13888, 18801, 24633, 31492, 39492, 48753, 59401, 71568, 87193, 104769, 126721, 151110, 178110, 207901, 243838, 283142, 326017, 372673, 423326, 478198, 537517, 606438, 680526
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
A114287 is the sum of the cubes of the cubeful numbers A046099. a(n) is prime for a(13) = 10513, a(45) = 1653409. a(n) is semiprime for n = 2, 8, 9, 12, 20, 30, 31, 32, 34, 37, 40, 47. a(n) is a perfect square for n = 0, 1, 2, 3, 4, 5, 6, 7, 10.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Cubefree.
|
|
FORMULA
|
a(n) = 1^3 + ... + A004709(n)^3. (Sum of the cubes of the cubeful numbers A046099 =< n) + (Sum of the cubes of the cube-free numbers A004709 =< n) = (Sum of the cubes of the numbers =< n) = A000537 = Sum of first n cubes; or n-th triangular number squared = (A000217(n))^2.
|
|
EXAMPLE
|
1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 9^3 + 10^3 + 11^3 = 3844 = 2^2 * 31^2.
|
|
CROSSREFS
|
Cf. A000217, A000537, A004709, A005117, A013929, A046099, A111715, A111732, A114287.
Sequence in context: A066647 A085037 A000537 this_sequence A098928 A139469 A103158
Adjacent sequences: A114283 A114284 A114285 this_sequence A114287 A114288 A114289
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 20 2005
|
|
|
Search completed in 0.002 seconds
|
