A166407 a(n) = floor(3*(A166406(n)/A005408(n))).

-3, 1, 0, 3, -9, 3, 0, 6, 0, 3, 0, 9, -30, 1, 0, 9, 0, 6, 0, 12, 0, 3, 0, 15, -63, 6, 0, 12, 0, 9, 0, 6, 0, 3, 0, 21, 0, 2, 0, 15, -81, 9, 0, 18, 0, 6, 0, 24, 0, 0, 0, 15, 0, 9, 0, 24, 0, 6, 0, 30, -165, 6, 0, 15, 0, 15, 0, 6, 0, 9, 0, 30, 0, 0, 0, 21, 0, 12, 0, 30, 0, 3, 0, 33, -234, 6, 0, 6

Offset: 0

Author

Antti Karttunen, Oct 21 2009

Keywords

• sign

Comments

Conjecture: the quotient A166406(i)/A005408(i) has denominator 3 when i is one of the terms of A166101, and it is integral in other cases. If true, then floor in the formula is unnecessary.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65535

Crossrefs

Cf. A166408.

Programs

Python

from sympy import floor, jacobi_symbol as J
def a(n):
    l=0
    m=0
    for i in range(1, 2*n + 2):
        if J(i, 2*n + 1)==-1: l+=i
        elif J(i, 2*n + 1)==1: m+=i
    return floor(3*((l - m)/(2*n + 1)))
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 12 2017