A111732 Sum of the squares of the first n nonsquarefree numbers (A013929).

0, 16, 80, 161, 305, 561, 885, 1285, 1861, 2486, 3215, 3999, 5023, 6319, 7919, 9855, 11880, 14184, 16585, 19085, 21789, 24705, 27841, 31441, 35410, 39506, 44130, 49314, 54939, 60715, 67115, 73676, 80732, 88476, 96576, 105040, 114256, 123860

Offset

0,2

Comments

Prime for a(8) = 1861, a(12) = 5023, a(14) = 7919. Semiprime for n = 3, 4, 7, 10, 13, 22, 23, 25, 28, 29, 40, 47.

Links

Table of n, a(n) for n=0..37.

Eric Weisstein's World of Mathematics, Squarefree.

Formula

a(n) = A013929(1) + ... A013929(n). (Sum of the squares of the nonsquarefree numbers <= n) + (Sum of the squares of the squarefree numbers <= n) = (Sum of the squares of the numbers <= n) = A000330(n) = Square pyramidal numbers: 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2n+1)/6.

Example

a(10) = 4^2 + 8^2 + 9^2 + 12^2 + 16^2 + 18^2 + 20^2 + 24^2 + 25^2 + 27^2 = 3215.

Crossrefs

Cf. A000330, A005117, A013929, A111715.

Sequence in context: A269584 A044203 A044584 * A271992 A008511 A130810

Adjacent sequences: A111729 A111730 A111731 * A111733 A111734 A111735

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 18 2005

Status

approved