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%I #38 Sep 21 2022 23:27:31
%S 1,7,31,37,67,73,97,103,127,157,199,202,229,241,247,262,277,283,307,
%T 313,331,337,346,367,379,382,397,409,427,457,472,487,499,517,547,562,
%U 577,607,619,643,661,667,682,697,727,757,769,787
%N Numbers k such that sigma(2*k+1) >= sigma(2*k).
%C The function A(x) enumerating the terms not exceeding x has the property that lim_{x->oo} A(x)/x exists (Hildebrand, 1990).
%D M. Laub, Advanced Problems: 6555. The American Mathematical Monthly, 94(8), 800 (1987). doi:10.2307/2323430.
%H Giuseppe Melfi, <a href="/A325423/b325423.txt">Table of n, a(n) for n = 1..2763</a>
%H Mits Kobayashi, Tim Trudgian, <a href="https://arxiv.org/abs/1904.10064">On integers n for which sigma(2n+1)>=sigma(2n)</a>, arXiv:1904.10064 [math.NT], 2019.
%H M. Laub & L. Mattics, <a href="https://www.jstor.org/stable/2324532">Problem 6555: Odd Integers with Relatively Large Divisor Sum</a>, The American Mathematical Monthly, 97(4), 351-353 (1990). doi:10.2307/2324532.
%F a(n) ~ c*n with 18.2 < c < 18.6 (claimed by Kobayashi and Trudgian).
%e 7 is in the sequence because sigma(14) = 1+2+7+14 = 24 <= sigma(15) = 1+3+5+15 = 24;
%e 31 is in the sequence because sigma(62) = 1+2+31+62 = 96 <= sigma(63) = 1+3+7+9+21+63 = 104.
%t Position[Partition[DivisorSigma[1,Range[2,1601]],2],_?(#[[2]] >= #[[1]]&),1,Heads->False]//Flatten (* _Harvey P. Dale_, Jan 10 2022 *)
%o (PARI) isok(n) = sigma(2*n+1) >= sigma(2*n); \\ _Michel Marcus_, Sep 09 2019
%Y Cf. A082957.
%K nonn
%O 1,2
%A _Giuseppe Melfi_, Sep 06 2019
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