A058208 a(n) = floor(6*n*sqrt(n)/Pi^2) - sigma(n), where sigma(n) is the sum of the divisors of n (A000203).

-1, -2, -1, -3, 0, -4, 3, -2, 3, 1, 10, -3, 14, 7, 11, 7, 24, 7, 30, 12, 26, 26, 43, 11, 44, 38, 45, 34, 64, 27, 72, 47, 67, 66, 77, 40, 98, 82, 92, 63, 117, 69, 127, 93, 105, 117, 147, 78, 151, 121, 149, 129, 180, 121, 175, 134, 181, 178, 215, 114, 227, 200

Offset: 1

Author

N. J. A. Sloane, Nov 29 2000

Keywords

• sign

Comments

Always > 0 for n > 12.

References

• József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter III, p. 77, section III.1.1.c.

Crossrefs

Cf. A000203, A057641, A055682, A059956.

Programs

Mathematica

a[n_] := Floor[n * Sqrt[n] / Zeta[2]] - DivisorSigma[1, n]; Array[a, 100] (* Amiram Eldar, Apr 23 2024 *)

PARI

a(n)=6*n*sqrt(n)\Pi^2 - sigma(n) \\ Charles R Greathouse IV, Feb 14 2013