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

1,1

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

Links

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

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000203, A008585, A013661, A023199.

Sequence in context: A138181 A006447 A014237 * A053079 A326061 A348203

Adjacent sequences: A033882 A033883 A033884 * A033886 A033887 A033888

Keyword

sign,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Jun 01 2000

Status

approved