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First differences of chowla(n).
2

%I #15 Oct 27 2023 22:00:45

%S 0,0,2,-2,5,-5,6,-3,4,-7,15,-15,9,-1,6,-14,20,-20,21,-11,3,-13,35,-30,

%T 10,-3,15,-27,41,-41,30,-16,5,-7,42,-54,21,-5,33,-49,53,-53,39,-7,-7,

%U -25,75,-68,35,-22,25,-45,65,-49,47,-41,9,-31,107,-107,33,7,22,-44,59,-77,57,-31

%N First differences of chowla(n).

%C Second differences give A053223, for n>1.

%C If the first term is changed to 1, this is also the first differences of A001065. - _N. J. A. Sloane_, Jan 17 2023

%H G. C. Greubel, <a href="/A053246/b053246.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A053222(n) - 1, for n>1

%p with(numtheory): seq( sigma(i+1) - sigma(i) - 1, i=2..100); # for n>1

%t Chowlan[n_] := If[n == 1, 0, DivisorSigma[1, n] - n - 1]; Table[Chowlan[n + 1] - Chowlan[n], {n, 1, 100}] (* _G. C. Greubel_, Sep 03 2018 *)

%t Differences[Join[{0},Table[DivisorSigma[1,n]-n-1,{n,2,100}]]] (* _Harvey P. Dale_, Dec 19 2022 *)

%o (Magma) [0] cat [DivisorSigma(1,n+1) - DivisorSigma(1,n) - 1: n in [2..100]]; // _G. C. Greubel_, Sep 03 2018

%o (PARI) concat([0], vector(100, n, n++; sigma(n+1) - sigma(n) -1)) \\ _G. C. Greubel_, Sep 03 2018

%Y Cf. A048050, A053222, A053223.

%Y Cf. also A001065.

%K sign

%O 1,3

%A _Asher Auel_, Jan 10 2000