A053246 First differences of chowla(n).

0, 0, 2, -2, 5, -5, 6, -3, 4, -7, 15, -15, 9, -1, 6, -14, 20, -20, 21, -11, 3, -13, 35, -30, 10, -3, 15, -27, 41, -41, 30, -16, 5, -7, 42, -54, 21, -5, 33, -49, 53, -53, 39, -7, -7, -25, 75, -68, 35, -22, 25, -45, 65, -49, 47, -41, 9, -31, 107, -107, 33, 7, 22, -44, 59, -77, 57, -31

Offset: 1

Author

Asher Auel, Jan 10 2000

Keywords

• sign

Comments

Second differences give A053223, for n>1.

If the first term is changed to 1, this is also the first differences of A001065. - N. J. A. Sloane, Jan 17 2023

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A048050, A053222, A053223.

Cf. also A001065.

Programs

Magma

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

Maple

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

Mathematica

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 *)
Differences[Join[{0},Table[DivisorSigma[1,n]-n-1,{n,2,100}]]] (* Harvey P. Dale, Dec 19 2022 *)

PARI

concat([0], vector(100, n, n++; sigma(n+1) - sigma(n) -1)) \\ G. C. Greubel, Sep 03 2018

Formula

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