A053223 Second differences of sigma(n).

-1, 2, -4, 7, -10, 11, -9, 7, -11, 22, -30, 24, -10, 7, -20, 34, -40, 41, -32, 14, -16, 48, -65, 40, -13, 18, -42, 68, -82, 71, -46, 21, -12, 49, -96, 75, -26, 38, -82, 102, -106, 92, -46, 0, -18, 100, -143, 103, -57, 47, -70, 110, -114, 96, -88, 50, -40, 138, -214, 140, -26, 15, -66

Offset: 1

Author

Asher Auel, Jan 06 2000

Keywords

• sign

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A053222, A053228, A053229, A053247, A053248.

Indices of 0: A099632 - 1.

Programs

Magma

[DivisorSigma(1, n+2) - 2*DivisorSigma(1,n+1) + DivisorSigma(1, n): n in [1..100]]; // G. C. Greubel, Sep 03 2018

Mathematica

Table[DivisorSigma[1,n+2] - 2*DivisorSigma[1,n+1] + DivisorSigma[1,n], {n,1,100}] (* G. C. Greubel, Sep 03 2018 *)

PARI

a(n)=sigma(n+2)-2*sigma(n+1)+sigma(n) \\ Charles R Greathouse IV, Mar 09 2014

Formula

G.f.: -1 - 1/x + (1 - x)^2*Sum_{k>=1} k*x^(k-2)/(1 - x^k). - Ilya Gutkovskiy, Jan 29 2017