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A053224 Numbers k for which sigma(k) < sigma(k+1).

%I A053224 #30 Oct 27 2023 22:00:45
%S A053224 1,2,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,47,49,
%T A053224 51,53,55,57,59,61,62,63,65,67,69,71,73,74,75,77,79,81,83,85,87,89,91,
%U A053224 93,95,97,99,101,103,107,109,111,113,115,119,121,123,125,127,129,131
%N A053224 Numbers k for which sigma(k) < sigma(k+1).
%C A053224 The asymptotic density of this sequence is 1/2 (Erdős, 1936). - _Amiram Eldar_, Mar 19 2021
%H A053224 Reinhard Zumkeller, <a href="/A053224/b053224.txt">Table of n, a(n) for n = 1..10000</a>
%H A053224 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 A053224 with(numtheory): seq( `if`(sigma(i) < sigma(i+1),i,[][]), i=1..134);
%t A053224 Select[Range[150], DivisorSigma[1, #] < DivisorSigma[1, # + 1] &] (* _Carl Najafi_, Aug 16 2011 *)
%o A053224 (Haskell)
%o A053224 import Data.List (elemIndices)
%o A053224 a053224 n = a053224_list !! (n-1)
%o A053224 a053224_list = map (+ 1) $ elemIndices True $
%o A053224    zipWith (<) a000203_list $ tail a000203_list
%o A053224 -- _Reinhard Zumkeller_, May 07 2012
%o A053224 (PARI) is(n)=sigma(n)<sigma(n+1) \\ _Charles R Greathouse IV_, Mar 09 2014
%Y A053224 Cf. A000203, A053222, A053226, A053230 (first differences).
%K A053224 nonn
%O A053224 1,2
%A A053224 _Asher Auel_, Jan 06 2000