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A058344
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Difference between the sum of the odd aliquot divisors of n and the sum of the even aliquot divisors of n.
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0
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0, 1, 1, -1, 1, 2, 1, -5, 4, 4, 1, -8, 1, 6, 9, -13, 1, 5, 1, -10, 11, 10, 1, -28, 6, 12, 13, -12, 1, 6, 1, -29, 15, 16, 13, -29, 1, 18, 17, -38, 1, 10, 1, -16, 33, 22, 1, -68, 8, 19, 21, -18, 1, 14, 17, -48, 23, 28, 1, -60, 1, 30, 41, -61, 19, 18, 1, -22, 27, 22, 1, -97, 1, 36, 49, -24, 19, 22, 1, -94, 40
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| The number of terms where the sum of the odd parts is greater than the sum of the even parts up to 10^n: 6, 57, 521, 5070, 50223, 500707, 5002236, ...,.
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FORMULA
| G.f.: Sum_{k>0} -(-1)^k*k*x^(2k)/(1-x^k). (Somos)
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EXAMPLE
| a(28) = -12 because the sum of the even divisors of 28 (2, 4 and 14) = 20 and the sum of the odd divisors of 28 (1 and 7) = 8.
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MATHEMATICA
| f[n_Integer] := Block[{d = Most[Divisors[n]]}, Plus @@ (-d*(-1)^d)]; Table[ f[n], {n, 81}] (* or *)
Rest[ CoefficientList[ Series[ Sum[ -(-1)^k*k*x^(2k)/(1 - x^k), {k, 100}], {x, 0, 81}], x]] (* Robert G. Wilson v, Aug 26 2005 *)
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PROG
| (PARI) a(n) = if(n<1, 0, sumdiv(n, d, (d<n)*d*-(-1)^d)) (Somos)
(PARI) {a(n)=if(n<1, 0, polcoeff( sum(k=1, n\2, -(-1)^k*k*x^(2*k)/(1-x^k), x*O(x^n)), n))} (Somos)
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CROSSREFS
| Cf. A002129.
Sequence in context: A061579 A094064 A159930 * A010582 A171175 A176053
Adjacent sequences: A058341 A058342 A058343 * A058345 A058346 A058347
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KEYWORD
| sign
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 14 2000
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EXTENSIONS
| Signs added by Michael Somos, Aug 21 2005
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