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 A053222 First differences of sigma(n). 17
 2, 1, 3, -1, 6, -4, 7, -2, 5, -6, 16, -14, 10, 0, 7, -13, 21, -19, 22, -10, 4, -12, 36, -29, 11, -2, 16, -26, 42, -40, 31, -15, 6, -6, 43, -53, 22, -4, 34, -48, 54, -52, 40, -6, -6, -24, 76, -67, 36, -21, 26, -44, 66, -48, 48, -40, 10, -30, 108, -106, 34, 8, 23, -43, 60, -76, 58 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(A002961(n)) = 0. - Reinhard Zumkeller, Dec 28 2011 Considering the values |a(n)| <= 100 for n < 10^13, we notice that some odd values do not appear within that range, namely 9, 17, 25, 27, 33, 37, 39, 45, 47, 49, 51, 55, 57, 59, 69, 71, 77, 81, 83, 87, 89, 91, 95, 97, and 99. All the other absolute values <= 100 appear for n < 3600, with the exception of a(1159742043) = 62. - Giovanni Resta, Jun 26 2017 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A000203(n+1) - A000203(n). G.f.:  2*(x-1)/(Q(0) -  2*x^2 + 2*x), where Q(k)= (2*x^(k+2) - x - 1)*k - 1 - 2*x + 3*x^(k+2) - x*(k+3)*(k+1)*(1-x^(k+2))^2/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, May 16 2013 G.f.: -1 + (1 - x)*Sum_{k>=1} k*x^(k-1)/(1 - x^k). - Ilya Gutkovskiy, Jan 29 2017 MAPLE A053222 := proc(n) numtheory[sigma](n+1)-numtheory[sigma](n) ; end proc: # R. J. Mathar, Jul 08 2013 MATHEMATICA DivisorSigma[1, Range[100]] // Differences (* Jean-François Alcover, Jan 26 2018 *) PROG (Haskell) a053222 n = a053222_list !! (n-1) a053222_list = zipWith (-) (tail a000203_list) a000203_list -- Reinhard Zumkeller, Oct 16 2011 (PARI) a(n)=sigma(n+1)-sigma(n) \\ Charles R Greathouse IV, Mar 09 2014 (GAP) List([1..70], n -> Sigma(n+1)-Sigma(n)); # Muniru A Asiru, Feb 14 2018 (MAGMA) [DivisorSigma(1, n+1) - DivisorSigma(1, n): n in [1..100]]; // G. C. Greubel, Sep 03 2018 CROSSREFS Cf. A000203, A053223, A053225, A053227, A053224, A053226. Sequence in context: A034869 A205858 A340793 * A351159 A318762 A262598 Adjacent sequences:  A053219 A053220 A053221 * A053223 A053224 A053225 KEYWORD sign,look AUTHOR Asher Auel (asher.auel(AT)reed.edu), Jan 06 2000 STATUS approved

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Last modified August 14 17:36 EDT 2022. Contains 356122 sequences. (Running on oeis4.)