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A318738 Numbers n=2*k-1 where Sum_{j=1..k} (-1)^(j+1) * d(2*j-1) achieves a new negative record, with d(n) = number of divisors of n (A000005).

%I A318738 #9 Sep 13 2018 18:15:05
%S A318738 3,15,39,63,99,259,319,403,675,679,943,1615,1779,2919,4899,5775,7399,
%T A318738 7407,13475,13479,25635,29835,29839,44955,78463,78475,108927,108931,
%U A318738 126819,136959,136975,136983,244875,244879,256355,276675,276687,457275,530139
%N A318738 Numbers n=2*k-1 where Sum_{j=1..k} (-1)^(j+1) * d(2*j-1) achieves a new negative record, with d(n) = number of divisors of n (A000005).
%H A318738 Hugo Pfoertner, <a href="/A318738/b318738.txt">Table of n, a(n) for n = 1..282</a>
%e A318738 a(1) = 3, because s = d(1)-d(3) = 1-2 = -1 is the first negative record.
%e A318738 a(2) = 15, because s = d(1)-d(3)+d(5)-d(7)+d(9)-d(11)+d(13)-d(15) =
%e A318738 1-2+2-2+3-2+2-4 = -2 is the first sum less than -1.
%o A318738 (PARI) s=0;j=-1;smin=0;forstep(k=1,600000,2,j=-j;s=s+j*numdiv(k);if(s<smin,smin=s;print1(k,", ")))
%Y A318738 Cf. A000005, A099774, A318734, A318735, A318736, A318737.
%K A318738 nonn
%O A318738 1,1
%A A318738 _Hugo Pfoertner_, Sep 08 2018