A082895 Closest number to sigma(n) = A000203(n) which is divisible by n.

1, 4, 3, 8, 5, 12, 7, 16, 9, 20, 11, 24, 13, 28, 30, 32, 17, 36, 19, 40, 42, 44, 23, 72, 25, 52, 27, 56, 29, 60, 31, 64, 33, 68, 35, 108, 37, 76, 39, 80, 41, 84, 43, 88, 90, 92, 47, 144, 49, 100, 51, 104, 53, 108, 55, 112, 57, 116, 59, 180, 61, 124, 126, 128, 65, 132, 67, 136, 69

Offset: 1

Author

Labos Elemer, Apr 22 2003

Keywords

• nonn
• look

Comments

In the case of a tie, we round up. - Robert Israel, May 26 2019

Examples

			n=100: sigma[100]=217 is between 100=1.100 and 200=2.100
200 is closer to 217, so a[100]=200;
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A082893-A082900, A000203.

Programs

Maple

f:= proc(n) uses numtheory; n*floor((floor(n/2)+sigma(n))/n) end proc:
map(f, [$1..100]); # Robert Israel, May 26 2019

Mathematica

Table[n*Floor[(Floor[n/2]+DivisorSigma[1, n])/n], {n, 1, 100}]

PARI

a(n)=sigma(n)\/n*n \\ Charles R Greathouse IV, Feb 15 2013

Formula

a(n) = n*floor((floor(n/2)+sigma(n))/n).