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A054785
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a(n) = sigma(2n) - sigma(n), where sigma is the sum of divisors of n,A000203.
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24
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2, 4, 8, 8, 12, 16, 16, 16, 26, 24, 24, 32, 28, 32, 48, 32, 36, 52, 40, 48, 64, 48, 48, 64, 62, 56, 80, 64, 60, 96, 64, 64, 96, 72, 96, 104, 76, 80, 112, 96, 84, 128, 88, 96, 156, 96, 96, 128, 114, 124, 144, 112, 108, 160, 144, 128, 160, 120, 120, 192, 124, 128, 208
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/8 = 1.2337005... (A111003). -Amiram Eldar,Jan 19 2024
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EXAMPLE
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n=9: sigma(18)=18+9+6+3+2+1=39, sigma(9)=9+3+1=13, a(9)=39-13=26.
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MAPLE
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a:= proc(n) local e;
e:= 2^padic:-ordp(n, 2);
2*e*numtheory:-sigma(n/e)
end proc:
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MATHEMATICA
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Table[DivisorSigma[1, 2n]-DivisorSigma[1, n], {n, 70}] (*Harvey P. Dale,May 11 2014 *)
Table[CoefficientList[Series[-Log[EllipticTheta[4, 0, x]], {x, 0, 80}], x][[n + 1]] n, {n, 1, 80}] (*Benedict W. J. Irwin,Jul 05 2016 *)
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PROG
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(Magma) [DivisorSigma(1, 2*n) - DivisorSigma(1, n): n in [1..70]];Vincenzo Librandi,Oct 05 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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