A084698 Beginning with 1 the smallest multiple of n such that the n-th partial sum is a square.

1, 8, 27, 28, 80, 180, 252, 208, 441, 800, 891, 684, 1300, 2156, 2160, 784, 816, 1728, 912, 1920, 1008, 2112, 1104, 2304, 1200, 2496, 1296, 2688, 1392, 2880, 1488, 3072, 1584, 3264, 1680, 3456, 1776, 3648, 1872, 3840, 1968, 4032, 2064, 4224, 2160, 4416

Offset

1,2

Comments

Other sequences with every partial sum yielding a square are (1) a(n) = n^3, but n^3 (though a multiple of n) is not the smallest such number for n >3. (2) a(n) = 2n-1.

Links

Table of n, a(n) for n=1..46.

Formula

For n>16, a(n) = 48n if n is odd, 96n if n is even.

Example

a(4) = 28 as 1+8+27+28 = 64 = 8^2.

Crossrefs

Sequence in context: A070498 A364875 A358240 * A070497 A070496 A373837

Adjacent sequences: A084695 A084696 A084697 * A084699 A084700 A084701

Keyword

nonn

Author

Amarnath Murthy, Jun 05 2003

Extensions

Edited by Dean Hickerson, Jul 20 2003

Status

approved