A046522 a(n) = 2*floor(sqrt(n)) - d(n), where d(n) is the number of divisors of n (A000005).

1, 0, 0, 1, 2, 0, 2, 0, 3, 2, 4, 0, 4, 2, 2, 3, 6, 2, 6, 2, 4, 4, 6, 0, 7, 6, 6, 4, 8, 2, 8, 4, 6, 6, 6, 3, 10, 8, 8, 4, 10, 4, 10, 6, 6, 8, 10, 2, 11, 8, 10, 8, 12, 6, 10, 6, 10, 10, 12, 2, 12, 10, 8, 9, 12, 8, 14, 10, 12, 8, 14, 4, 14, 12, 10, 10, 12, 8, 14, 6

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Always >= 0.

References

• D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section II.1.1.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Programs

Maple

with(numtheory); f := n->2*floor(sqrt(n))-sigma[ 0 ](n);

Mathematica

Table[2Floor[Sqrt[n]]-DivisorSigma[0,n],{n,80}] (* Harvey P. Dale, Nov 27 2013 *)

PARI

a(n)={2*sqrtint(n)-numdiv(n)} \\ Andrew Howroyd, Mar 07 2020