A055682 a(n) = floor(n*sqrt(n)) - sigma(n), where sigma(n) is the sum of the divisors of n (A000203).

0, -1, 1, 1, 5, 2, 10, 7, 14, 13, 24, 13, 32, 28, 34, 33, 52, 37, 62, 47, 64, 67, 86, 57, 94, 90, 100, 92, 126, 92, 140, 118, 141, 144, 159, 125, 187, 174, 187, 162, 220, 176, 237, 207, 223, 239, 274, 208, 286, 260, 292, 276, 331, 276, 335, 299

Offset: 1

Author

N. J. A. Sloane, Nov 29 2000

Keywords

• sign

Comments

Always > 0 for n > 2.

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.b.

Links

• C. C. Lindner, Problem E1888, Amer. Math. Monthly, 73 (1966), 538; solution by A. Bager and S. Russ, op. cit. 74 (1967), 1143.
• N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 6.

Crossrefs

Cf. A000203, A057641, A058208.

Programs

Mathematica

a[n_] :=  Floor[n*Sqrt[n]] - DivisorSigma[1, n]; Array[a, 100] (* Amiram Eldar, Apr 25 2024 *)

PARI

a(n)=sqrtint(n^3)-sigma(n) \\ Charles R Greathouse IV, Feb 14 2013