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URL: https://oeis.org/A053223

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A053223
Second differences of sigma(n).
11
-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
1,2
FORMULA
G.f.: -1 - 1/x + (1 - x)^2*Sum_{k>=1} k*x^(k-2)/(1 - x^k). - Ilya Gutkovskiy, Jan 29 2017
MATHEMATICA
Table[DivisorSigma[1, n+2] - 2*DivisorSigma[1, n+1] + DivisorSigma[1, n], {n, 1, 100}] (* G. C. Greubel, Sep 03 2018 *)
Differences[DivisorSigma[1, Range[70]], 2] (* Harvey P. Dale, Nov 23 2025 *)
PROG
(PARI) a(n)=sigma(n+2)-2*sigma(n+1)+sigma(n) \\ Charles R Greathouse IV, Mar 09 2014
(Magma) [DivisorSigma(1, n+2) - 2*DivisorSigma(1, n+1) + DivisorSigma(1, n): n in [1..100]]; // G. C. Greubel, Sep 03 2018
CROSSREFS
Indices of 0: A099632 - 1.
Sequence in context: A034702 A325745 A167206 * A153383 A278997 A342782
KEYWORD
sign
AUTHOR
Asher Auel, Jan 06 2000
STATUS
approved