A033885 - OEIS

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

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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