A318737 Numbers n=2*k-1 where Sum_{j=1..k} (-1)^(j+1) * d(2*j-1) achieves a new record, with d(n) = number of divisors of n (A000005).

1, 9, 25, 49, 85, 133, 169, 225, 445, 845, 973, 1125, 2205, 2209, 2469, 2829, 7929, 9429, 9945, 23569, 24073, 24645, 26145, 40425, 68153, 71289, 72413, 89517, 112233, 112245, 128973, 162405, 162409, 162429, 297073, 477489, 477493, 502713, 561253

Offset: 1

Author

Hugo Pfoertner, Sep 05 2018

Keywords

• nonn

Examples

			a(2) = 9, because s = d(1)-d(3)+d(5)-d(7)+d(9) = 1-2+2-2+3 = 2 exceeds d(1)=1, d(1)-d(3)=-1, d(1)-d(3)+d(5)=1, d(1)-d(3)+d(5)-d(7)=-1.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..268

Crossrefs

Cf. A000005, A099774, A318734, A318735, A318736, A318738.

Programs

PARI

s=0;smax=0;j=-1;forstep(k=1,600000,2,j=-j;s=s+j*numdiv(k);if(s>smax,smax=s;print1(k,", ")))