A057022 a(n) = floor((sum of divisors of n) / (number of divisors of n)), or floor(sigma_1(n)/sigma_0(n)).

1, 1, 2, 2, 3, 3, 4, 3, 4, 4, 6, 4, 7, 6, 6, 6, 9, 6, 10, 7, 8, 9, 12, 7, 10, 10, 10, 9, 15, 9, 16, 10, 12, 13, 12, 10, 19, 15, 14, 11, 21, 12, 22, 14, 13, 18, 24, 12, 19, 15, 18, 16, 27, 15, 18, 15, 20, 22, 30, 14, 31, 24, 17, 18, 21, 18, 34, 21, 24, 18

Offset

1,3

Comments

Floor of mean of divisors of n. - Jon E. Schoenfield, Dec 24 2016

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = (A000203(n) - A054025(n))/A000005(n).

Example

a(4)=2 since the 3 divisors of 4 are 1, 2 and 4 and floor((1 + 2 + 4)/3) = floor(7/3) = 2.

Mathematica

Floor[Table[Total[Divisors[n]]/Length[Divisors[n]], {n, 20}]] (* Daniel Jolly, Nov 15 2014 *)
Table[Floor[DivisorSigma[1, n]/DivisorSigma[0, n]], {n, 70}] (* Harvey P. Dale, Jan 14 2015 *)

Prog

(Haskell)
a057022 n = a000203 n `div` a000005 n
-- Reinhard Zumkeller, Jan 06 2012
(PARI) a(n) = sigma(n)\numdiv(n); \\ Michel Marcus, Nov 15 2014

Crossrefs

Cf. A000005, A000203, A009205, A054025, A057020, A057021.

Cf. A003601.

Sequence in context: A100197 A368314 A356874 * A287896 A087504 A067539

Adjacent sequences: A057019 A057020 A057021 * A057023 A057024 A057025

Keyword

nonn

Author

Henry Bottomley, Jul 21 2000

Status

approved