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A053226 Numbers k for which sigma(k) > sigma(k+1).

%I A053226 #23 Oct 27 2023 22:00:45
%S A053226 4,6,8,10,12,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,45,46,48,50,
%T A053226 52,54,56,58,60,64,66,68,70,72,76,78,80,82,84,86,88,90,92,94,96,98,
%U A053226 100,102,104,105,106,108,110,112,114,116,117,118,120,122,124,126,128,130
%N A053226 Numbers k for which sigma(k) > sigma(k+1).
%C A053226 The asymptotic density of this sequence is 1/2 (Erdős, 1936). - _Amiram Eldar_, Mar 19 2021
%H A053226 T. D. Noe, <a href="/A053226/b053226.txt">Table of n, a(n) for n = 1..1000</a>
%H A053226 Paul Erdős, <a href="https://doi.org/10.1017/S0305004100019277">On a problem of Chowla and some related problems</a>, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 32, No. 4 (1936), pp. 530-540; <a href="https://old.renyi.hu/~p_erdos/1936-03.pdf">alternative link</a>.
%p A053226 with(numtheory): seq( `if`((sigma(i) > sigma(i+1)),i,print( )), i=1..139);
%t A053226 Select[Range[150], DivisorSigma[1, #] > DivisorSigma[1, # + 1] &] (* _Carl Najafi_, Aug 16 2011 *)
%o A053226 (Haskell)
%o A053226 import Data.List (findIndices)
%o A053226 a053226 n = a053226_list !! (n-1)
%o A053226 a053226_list = map (+ 1) $ findIndices (< 0) a053222_list
%o A053226 -- _Reinhard Zumkeller_, Oct 16 2011
%o A053226 (PARI) is(n)=sigma(n)>sigma(n+1) \\ _Charles R Greathouse IV_, Mar 09 2014
%Y A053226 Cf. A000203, A053222, A053224, A053238.
%K A053226 nonn
%O A053226 1,1
%A A053226 _Asher Auel_, Jan 06 2000