A066518 - OEIS

A066518

Anti-divisor class sums of n.

0, 0, 0, -1, 1, 0, -2, 2, 0, -2, 2, -1, -1, 2, 0, -2, 0, 2, -2, 2, 0, -4, 4, -1, -1, 2, -2, 0, 2, 0, -4, 2, 2, -2, 2, 0, -4, 2, 2, -3, 3, -2, 0, 2, -2, 0, 0, 2, -4, 4, 0, -6, 6, 0, -2, 2, -2, -2, 2, 1, -1, 0, 2, -2, 2, -2, -4, 6, 0, -2, 0, 0, -2, 4, 0, -4, 2, 2, -2, 0, 2, -6, 6, -1, -3, 4, -4, 2, 2, 0, -2, 0, 0, -4, 6, 0, -6, 6, 0, -2, 0, 0, -2

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OFFSET

1,7

COMMENTS

An anti-divisor of n is an integer d in [2,n-1] such that n == (d-1)/2, d/2, or (d+1)/2 (mod d), the class of d being -1, 0, or 1, respectively. The class sum of n is the sum of the classes of all of its anti-divisors.

See A066272 for definition of anti-divisor.

LINKS

Table of n, a(n) for n=1..103.

Jon Perry, Class sums

FORMULA

f(n)=sum(ad class)

EXAMPLE

The ad's of 10 are 3, 4 and 7, with classes -1, 0 and -1, so f(10)=-2.

MATHEMATICA

a[n_ ] := Sum[Which[Mod[n, d]==(d-1)/2, -1, Mod[n, d]==(d+1)/2, 1, True, 0], {d, 2, n-1}]

CROSSREFS

Cf. A066519.