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
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
KEYWORD
sign,look
AUTHOR
Asher Auel, Jan 06 2000
STATUS
approved