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A071323
Alternating sum of all divisors of n; divisors nondecreasing, starting with 1.
4
1, -1, -2, 3, -4, -4, -6, -5, 7, -6, -10, -8, -12, -8, -12, 11, -16, -13, -18, -12, -16, -12, -22, -16, 21, -14, -20, -18, -28, -22, -30, -21, -24, -18, -32, 25, -36, -20, -28, -24, -40, -32, -42, -30, -36, -24, -46, -32, 43
OFFSET
1,3
COMMENTS
a(n)>0 iff n square (iff A000005(n) is even), a(A000290(n))>0;
for primes p: a(p) = 1 - p.
LINKS
EXAMPLE
Divisors of 20 are {1,2,4,5,10,20}, therefore a(20) = 1 - 2 + 4 - 5 + 10 - 20 = -12.
MATHEMATICA
Table[Total[Times@@@Partition[Riffle[Divisors[n], {1, -1}, {2, -1, 2
}], 2]], {n, 50}] (* Harvey P. Dale, Nov 05 2014 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Reinhard Zumkeller, May 18 2002
STATUS
approved