A079546 a(n) = sigma(n) - 4*phi(n).

-3, -1, -4, -1, -10, 4, -16, -1, -11, 2, -28, 12, -34, 0, -8, -1, -46, 15, -52, 10, -16, -4, -64, 28, -49, -6, -32, 8, -82, 40, -88, -1, -32, -10, -48, 43, -106, -12, -40, 26, -118, 48, -124, 4, -18, -16, -136, 60, -111, 13, -56, 2, -154, 48, -88, 24, -64, -22, -172, 104, -178, -24, -40, -1, -108, 64, -196, -2, -80, 48, -208, 99, -214

Offset: 1

Author

N. J. A. Sloane, Jan 23 2003

Keywords

• sign
• easy

Comments

If k is even and a(k) = 0 then sigma(2*k) >= 4*k, i.e., 2*k is nondeficient (A023196) (Makowski, 1987). - Amiram Eldar, Dec 05 2023

References

• Andrzej Makowski, Remarks on some problems in the elementary theory of numbers, Acta Math. Univ. Comenian 50/51 (1987), 277-281.
• József Sándor, Dragoslav S. Mitrinović, and Borislav Crstici, Handbook of Number Theory I, Springer, 2005, Chapter III, p. 88.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000203, A023196, A068390.

Programs

Magma

[DivisorSigma(1, n) - 4*EulerPhi(n): n in [1..80]]; // G. C. Greubel, Jun 19 2019

Mathematica

Table[DivisorSigma[1,n]-4*EulerPhi[n],{n,80}] (* Harvey P. Dale, Dec 08 2014 *)

PARI

vector(80, n, sigma(n) - 4*eulerphi(n)) \\ G. C. Greubel, Jun 19 2019

Sage

[sigma(n,1) - 4*euler_phi(n) for n in (1..80)] # G. C. Greubel, Jun 19 2019

Formula

Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/12 - 12/Pi^2 = -0.393387... . - Amiram Eldar, Dec 05 2023