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

1,2

Comments

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

Links

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

Formula

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

Example

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

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}]

Prog

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

Crossrefs

Cf. A082893-A082900, A000203.

Sequence in context: A280166 A257088 A022998 * A086938 A007015 A354139

Adjacent sequences: A082892 A082893 A082894 * A082896 A082897 A082898

Keyword

nonn,look

Author

Labos Elemer, Apr 22 2003

Status

approved