A227912 Sum of all k from {1,...,n} such that the fractional part of n/k is contained in the closed interval [1/4, 3/4].

0, 0, 2, 3, 9, 4, 14, 14, 19, 28, 24, 29, 41, 51, 54, 49, 67, 74, 89, 87, 99, 110, 120, 125, 142, 154, 169, 178, 180, 211, 197, 223, 262, 261, 285, 270, 299, 323, 342, 371, 359, 374, 422, 434, 477, 454, 478, 493, 538, 566, 555, 628, 606, 663, 666, 676, 716

Offset

1,3

Links

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

Example

a(6) = 4, only k = 4 satisfies the condition frac(6/k) is an element of [1/4, 3/4].

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. A227913.

Sequence in context: A089206 A329568 A249824 * A229212 A210586 A202017

Adjacent sequences: A227909 A227910 A227911 * A227913 A227914 A227915

Keyword

nonn

Author

Jon Perry, Oct 13 2013

Status

approved