A175908 3*sum(k=1..n, floor(k^2/n)) - n^2.

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

Offset: 1

Author

John W. Layman, Oct 14 2010

Keywords

• nonn

Comments

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]

Links

• Walter Blumberg, Problem 11529, Amer. Math. Monthly, 117 (2010), 742.

Crossrefs

Cf. A020893.

Programs

Maple

A175908:=n->3*add(floor(k^2/n),k=1..n)-n^2: seq(A175908(n), n=1..60); # Wesley Ivan Hurt, Jul 10 2014

Mathematica

Table[3 Sum[Floor[k^2/n], {k, n}] - n^2, {n, 60}] (* Wesley Ivan Hurt, Jul 10 2014 *)

PARI

a(n) = 3*sum(k=1, n, k^2\n) - n^2; \\ Michel Marcus, Jul 09 2014

Formula

a(n) = 3*A014817(n) - A000290(n). - Wesley Ivan Hurt, Jul 10 2014