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 A054785 a(n) = sigma(2n) - sigma(n), where sigma is the sum of divisors of n, A000203. 24
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sum of divisors of 2*n that do not divide n. - Franklin T. Adams-Watters, Oct 04 2018 a(n) = 2*n iff n = 2^k, k >= 0 (A000079). - Bernard Schott, Mar 24 2020 LINKS Paul Tek, Table of n, a(n) for n = 1..10000 Octavio A. Agustín-Aquino, Wang-Sun formula in GL(Z/2kZ), Integers, Vol. 23 (2023), #A37. FORMULA a(n) = A000203(2n) - A000203(n). a(n) = 2*A002131(n). a(2*n) = A000203(n) + A000593(2*n). - Reinhard Zumkeller, Apr 23 2008 L.g.f.: -log(EllipticTheta(4,0,x)) = Sum_{ n>0 } (a(n)/n)*x^n. - Benedict W. J. Irwin, Jul 05 2016 G.f.: Sum_{k>=1} 2*k*x^k/(1 - x^(2*k)). - Ilya Gutkovskiy, Oct 23 2018 Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/8 = 1.2337005... (A111003). - Amiram Eldar, Jan 19 2024 EXAMPLE n=9: sigma(18)=18+9+6+3+2+1=39, sigma(9)=9+3+1=13, a(9)=39-13=26. MAPLE a:= proc(n) local e; e:= 2^padic:-ordp(n, 2); 2*e*numtheory:-sigma(n/e) end proc: map(a, [\$1..100]); # Robert Israel, Jul 05 2016 MATHEMATICA 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 *) PROG (PARI) a(n)=sigma(2*n)-sigma(n) \\ Charles R Greathouse IV, Feb 13 2013 (Magma) [DivisorSigma(1, 2*n) - DivisorSigma(1, n): n in [1..70]]; Vincenzo Librandi, Oct 05 2018 CROSSREFS Cf. A000079, A000203, A000593, A111003, A002131, A320059. Sequence in context: A198346 A078750 A360156 * A236924 A266575 A260514 Adjacent sequences: A054782 A054783 A054784 * A054786 A054787 A054788 KEYWORD nonn,easy AUTHOR Labos Elemer, May 22 2000 STATUS approved

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Last modified July 17 08:16 EDT 2024. Contains 374360 sequences. (Running on oeis4.)