

A111732


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


2



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
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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

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



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



