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Search: id:A111732
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| A111732 |
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Sum of the squares of the first n not square-free numbers (A013929). |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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.
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LINKS
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Eric Weisstein's World of Mathematics, Squarefree.
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FORMULA
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a(n) = A013929(1) + ... A013929(n). (Sum of the squares of the not square-free numbers =< n) + (Sum of the squares of the square-free 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.
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EXAMPLE
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a(10) = 4^2 + 8^2 + 9^2 + 12^2 + 16^2 + 18^2 + 20^2 + 24^2 + 25^2 + 27^2 = 3215.
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CROSSREFS
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Cf. A005117, A013929, A111715.
Sequence in context: A061995 A044203 A044584 this_sequence A008511 A130810 A050468
Adjacent sequences: A111729 A111730 A111731 this_sequence A111733 A111734 A111735
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 18 2005
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