

A114286


Sum of the cubes of the first n cubefree numbers.


1



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
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OFFSET

0,3


COMMENTS

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

Table of n, a(n) for n=0..36.
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 cubefree numbers A004709 <= n) = (Sum of the cubes of the numbers <= n) = A000537 = Sum of first n cubes; or nth 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: A231686 A231688 A000537 * A098928 A139469 A103158
Adjacent sequences: A114283 A114284 A114285 * A114287 A114288 A114289


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Nov 20 2005


STATUS

approved



