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Numbers n such that n < sigma(n) - sigma(n-1).
2

%I #14 Jul 14 2024 20:12:31

%S 12,18,20,24,30,36,42,48,54,60,72,80,84,90,96,102,104,108,114,120,126,

%T 132,138,140,144,150,156,160,162,168,174,180,192,198,200,204,210,216,

%U 224,228,234,240,252,258,260,264,270,272,276,280,282,288,294,300,306

%N Numbers n such that n < sigma(n) - sigma(n-1).

%C Also numbers n such that antisigma(n) < antisigma(n-1), where antisigma(n) = A024816(n) = the sum of the non-divisors of n that are between 1 and n.

%C Numbers n such that A163553(n-1) < 0.

%C Numbers n such that antisigma(n) > antisigma(n-1) = A231711.

%C Numbers n such that antisigma(n) = antisigma(n-1) = A231545.

%C Complement of union of A231711, A231545 and number 1.

%C Does this sequence have a density? - _Charles R Greathouse IV_, Jul 14 2024

%H Jaroslav Krizek, <a href="/A231547/b231547.txt">Table of n, a(n) for n = 1..1000</a>

%e 12 is in sequence because antisigma(12) = 50 < antisigma(11) = 54.

%t Select[Range[350],#<(DivisorSigma[1,#]-DivisorSigma[1,#-1])&] (* _Harvey P. Dale_, May 26 2016 *)

%o (PARI) is(n)=n<sigma(n)-sigma(n-1) \\ _Charles R Greathouse IV_, Jul 14 2024

%Y Cf. A231545, A231546, A231711, A231548, A024816, A163553.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Nov 12 2013