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n for which second differences of sigma(n) are positive.
5

%I #10 Oct 27 2023 22:00:45

%S 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,46,48,50,

%T 52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,

%U 98,100,102,106,108,110,112,114,116,118,120,122,124,126,128,130,132

%N n for which second differences of sigma(n) are positive.

%H G. C. Greubel, <a href="/A053228/b053228.txt">Table of n, a(n) for n = 1..10000</a>

%p with(numtheory): seq(`if`(sigma(i+2)-sigma(i+1)>(sigma(i+1)-sigma(i)),i,print( )), i=1..142);

%t Select[Range[150], DivisorSigma[1, #+2] - DivisorSigma[1, #+1] > (DivisorSigma[1, # + 1] - DivisorSigma[1, #]) &] (* _G. C. Greubel_, Sep 03 2018 *)

%t Position[Differences[#,2]&/@Partition[DivisorSigma[1,Range[140]],3,1],_?(Positive[ #]&)][[All,1]] (* _Harvey P. Dale_, Jan 18 2023 *)

%Y Cf. A000203, A053223, A053229.

%K nonn

%O 1,1

%A _Asher Auel_, Jan 10 2000