A194750 - OEIS

A194750

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

1, 1, 1, 4, 3, 2, 1, 7, 5, 3, 11, 8, 5, 2, 13, 9, 5, 18, 13, 8, 3, 19, 13, 7, 25, 18, 11, 4, 25, 17, 9, 32, 23, 14, 5, 31, 21, 11, 1, 30, 19, 8, 39, 27, 15, 3, 37, 24, 11, 47, 33, 19, 5, 44, 29, 14, 55, 39, 23, 7, 51, 34, 17, 63, 45, 27, 9, 58, 39, 20, 71, 51, 31, 11, 65

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..75.

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 *)