A194751 - OEIS

A194751

Number of k such that {k*e} > {n*e}, where { } = fractional part.

0, 1, 2, 0, 2, 4, 6, 1, 4, 7, 0, 4, 8, 12, 2, 7, 12, 0, 6, 12, 18, 3, 10, 17, 0, 8, 16, 24, 4, 13, 22, 0, 10, 20, 30, 5, 16, 27, 38, 10, 22, 34, 4, 17, 30, 43, 10, 24, 38, 3, 18, 33, 48, 10, 26, 42, 2, 19, 36, 53, 10, 28, 46, 1, 20, 39, 58, 10, 30, 50, 0, 21, 42, 63, 10, 32

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..76.

MATHEMATICA

r = E; p[x_] := FractionalPart[x];

u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]

v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]

s[n_] := Sum[u[n, k], {k, 1, n}]

t[n_] := Sum[v[n, k], {k, 1, n}]

Table[s[n], {n, 1, 100}] (* A194750 *)