A227913 Sum of all k from {1,...,n} such that the fractional part of n/k is contained in the open interval (1/4, 3/4).

0, 0, 2, 3, 5, 4, 10, 14, 15, 20, 20, 29, 37, 43, 38, 49, 63, 66, 85, 71, 83, 102, 116, 125, 118, 146, 153, 162, 176, 179, 193, 223, 246, 253, 233, 254, 295, 315, 326, 339, 355, 342, 418, 418, 405, 446, 474, 493, 506, 518, 539, 612, 602, 631, 598, 644, 700

Offset

1,3

Comments

Differs from A227912 because the inequalities are strict.

Links

Table of n, a(n) for n=1..57.

Example

a(5)=5, the valid k such that frac(5/k) is an element of (1/4,3/4) are 2 and 3, 2+3=5.

Prog

(JavaScript)
for (i=1; i<50; i++) {
c=0;
for (j=1; j<=i; j++) {
v=Math.floor(i/j);
if (i/j-v>0.25 && i/j-v<0.75) c+=j;
}
document.write(c+", ");
;
}

Crossrefs

Cf. A227912.

Sequence in context: A066417 A347348 A254669 * A079521 A325549 A370895

Adjacent sequences: A227910 A227911 A227912 * A227914 A227915 A227916

Keyword

nonn

Author

Jon Perry, Oct 13 2013

Status

approved