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A175908
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3*sum(k=1..n, floor(k^2/n)) - n^2.
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2
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2, 2, 3, 5, 2, 3, 5, 8, 6, 2, 5, 9, 2, 5, 9, 14, 2, 6, 5, 11, 6, 5, 11, 18, 8, 2, 9, 11, 2, 9, 11, 20, 6, 2, 11, 21, 2, 5, 15, 20, 2, 6, 5, 17, 12, 11, 17, 30, 14, 8, 9, 11, 2, 9, 17, 26, 6, 2, 11, 27, 2, 11, 21, 32, 2, 6, 5, 17, 12, 11, 23, 36, 2, 2, 21, 17, 8, 15, 17, 38
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OFFSET
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1,1
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COMMENTS
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According to the reference, a(p*q) = a(p) + a(q) - 2 whenever p and q are distinct primes with p congruent to q modulo 4.
The sequences of indices n where a(n)=2 is {1, 2, 5, 10, 13, 17, 26, ...}, which appears to be A020893 (squarefree sums of two squares). This has been confirmed for the first 500 terms. [John W. Layman, May 16 2011]
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LINKS
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Walter Blumberg, Problem 11529, Amer. Math. Monthly, 117 (2010), 742.
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FORMULA
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MAPLE
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MATHEMATICA
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Table[3 Sum[Floor[k^2/n], {k, n}] - n^2, {n, 60}] (* Wesley Ivan Hurt, Jul 10 2014 *)
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PROG
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(PARI) a(n) = 3*sum(k=1, n, k^2\n) - n^2; \\ Michel Marcus, Jul 09 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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