A033885 a(n) = 3*n - sum of divisors of n.

2, 3, 5, 5, 9, 6, 13, 9, 14, 12, 21, 8, 25, 18, 21, 17, 33, 15, 37, 18, 31, 30, 45, 12, 44, 36, 41, 28, 57, 18, 61, 33, 51, 48, 57, 17, 73, 54, 61, 30, 81, 30, 85, 48, 57, 66, 93, 20, 90, 57, 81, 58, 105, 42, 93, 48, 91, 84, 117, 12, 121, 90, 85, 65, 111, 54, 133, 78, 111, 66

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign
• easy

Comments

The first zero term occurs at n = 120. The first negative term is a(180) = -6. For any k, k*n - sigma(n) is negative for some n. See A023199. - T. D. Noe, Aug 07 2003

Examples

			For n=4, 3n=12, sum of divisors of n is 1+2+4=7, so a(4)=12-7=5.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A008585, A013661, A023199.

Programs

Maple

with(numtheory): for n from 1 to 150 do printf(`%d,`,3*n-sigma(n)) od:

Mathematica

Table[3 n - DivisorSigma[1, n], {n, 70}] (* Ivan Neretin, Sep 30 2017 *)

PARI

a(n)=3*n-sigma(n) \\ Charles R Greathouse IV, Mar 16 2016

Formula

a(n) = A008585(n) - A000203(n). - Omar E. Pol, Sep 30 2017

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 3 - zeta(2) = 1.355065... . - Amiram Eldar, Mar 25 2024

Extensions

More terms from James Sellers, Jun 01 2000