A053247 -id:A053247 - cp's OEIS frontend

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

Asher Auel, Jan 06 2000

sign

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

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

Indices of 0: A099632 - 1.

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

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

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

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

A053248 Second differences of sigma(n) that are negative.

Original entry on oeis.org

1, 4, 10, 9, 11, 30, 10, 20, 40, 32, 16, 65, 13, 42, 82, 46, 12, 96, 26, 82, 106, 46, 18, 143, 57, 70, 114, 88, 40, 214, 26, 66, 136, 88, 120, 244, 30, 60, 160, 171, 47, 256, 36, 150, 266, 96, 40, 286, 88, 176, 226, 124, 12, 24, 342, 170, 230, 222, 94, 34, 443, 71

Offset: 1

Asher Auel, Jan 11 2000

nonn

Cf. A000203, A053223, A053247.

with (numtheory): f := [seq( sigma(i+2) - sigma(i+1) - (sigma(i+1) - sigma(i)), i=1..200)];
seq(`if`(f[i] < 0,f[i],print( )), i=1..200);

Abs[Select[Differences[DivisorSigma[1,Range[200]],2],Negative]] (* Harvey P. Dale, Aug 13 2015 *)

a(n) = A053223(A053229(n)).

cp's OEIS Frontend

A053223 Second differences of sigma(n).

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