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).

3, 15, 39, 63, 99, 259, 319, 403, 675, 679, 943, 1615, 1779, 2919, 4899, 5775, 7399, 7407, 13475, 13479, 25635, 29835, 29839, 44955, 78463, 78475, 108927, 108931, 126819, 136959, 136975, 136983, 244875, 244879, 256355, 276675, 276687, 457275, 530139

Offset: 1

Author

Hugo Pfoertner, Sep 08 2018

Keywords

• nonn

Examples

			a(1) = 3, because s = d(1)-d(3) = 1-2 = -1 is the first negative record.
a(2) = 15, because s = d(1)-d(3)+d(5)-d(7)+d(9)-d(11)+d(13)-d(15) =
1-2+2-2+3-2+2-4 = -2 is the first sum less than -1.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..282

Crossrefs

Cf. A000005, A099774, A318734, A318735, A318736, A318737.

Programs

PARI

s=0;j=-1;smin=0;forstep(k=1,600000,2,j=-j;s=s+j*numdiv(k);if(s