A103502 Floor of Sum_{p prime <= n} (fractional part of n/p).

0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 2, 2, 3, 3, 2, 2, 3, 2, 3, 2, 3, 2, 4, 3, 4, 5, 4, 4, 3, 3, 4, 4, 4, 3, 5, 3, 5, 5, 4, 4, 6, 5, 6, 6, 5, 5, 7, 6, 6, 6, 5, 5, 7, 5, 7, 7, 6, 7, 7, 6, 7, 7, 7, 6, 7, 7, 9, 8, 8, 8, 8, 7, 8, 8, 9, 9, 10, 9, 9, 9, 8, 8, 10, 9, 9, 8, 8, 8, 8, 8, 9, 9, 9, 9, 11, 9, 11

Offset: 1

Author

Carlos Alves, Feb 08 2005

Keywords

• nonn

Examples

			a(5) = [{5/2}+{5/3}+{5/5}] = [1/2 + 2/3 + 0] = 1.
a(6) = [{6/2}+{6/3}+{6/5}] = [0 + 0 + 1/5] = 0.
		

Programs

Mathematica

f[n_] := Floor[Plus @@ FractionalPart[n / Table[Prime[i], {i, PrimePi[ n]}]]]; Table[ f[n], {n, 103}]

PARI

a(n) = {s = 0; forprime(p = 2, n, s+= frac(n/p);); floor(s);} \\ Michel Marcus, Feb 05 2014

Extensions

More terms from Robert G. Wilson v, Feb 11 2005

Offset corrected by Michel Marcus, Feb 05 2014