|
Search: id:A114287
|
|
|
| A114287 |
|
Sum of the cubes of the first n cubeful numbers. |
|
+0
2
|
|
| 0, 512, 4608, 18432, 38115, 70883, 134883, 245475, 402939, 578555, 840699, 1213947, 1725947, 2257388, 2938860, 3823596, 4948460, 6208172, 7613100, 9341100, 11294225, 13391377, 15851752, 18367208, 21353192, 24865000, 28961000
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
A114286 is the sum of the cubes of the cubefree numbers A004709. a(n) is prime for a(12) = 1725947, a(52) = 437508377, a(53) = 471520601. a(n) is semiprime for n = 5, 21, 31, 36, 37, 49.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Cubefree.
|
|
FORMULA
|
a(n) = A046099(1)^3 + ... + A046099(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
|
a(10) = 8^3 + 16^3 + 24^3 + 27^3 + 32^3 + 40^3 + 48^3 + 54^3 + 56^3 + 64^3
= 840699.
|
|
CROSSREFS
|
Cf. A000217, A000537, A004709, A005117, A013929, A046099, A111715, A111732, A114286.
Adjacent sequences: A114284 A114285 A114286 this_sequence A114288 A114289 A114290
Sequence in context: A135273 A016995 A017067 this_sequence A061209 A017259 A017367
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 20 2005
|
|
|
Search completed in 0.002 seconds
|
