A108775 a(n) = floor(sigma(n)/n).

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1

Offset: 1

Author

Franz Vrabec, Jun 27 2005

Keywords

• nonn

Comments

The sequence is unbounded. - Vrabec

First occurrence of k: 1,6,120,27720,..., which is A023199. - Robert G. Wilson v, Jun 28 2005

a(n) > 1 if n is perfect or abundant. a(n) = 2 if n is perfect or primitive abundant (see A091191). - Alonso del Arte, Feb 06 2012

Examples

			a(6) = 2 because sigma(6)/6 = (1 + 2 + 3 + 6)/6 = 2.
		

References

• W. Sierpinski, Elementary Theory of Numbers, 1987, p. 174 ff.

Links

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

Crossrefs

Cf. A000203, A054024.

Cf. A017665, A017666.

Programs

Haskell

a108775 n = div (a000203 n) n  -- Reinhard Zumkeller, Mar 23 2013

Mathematica

Table[ Floor[ DivisorSigma[1, n]/n], {n, 105}] (* Robert G. Wilson v, Jun 28 2005 *)

PARI

a(n) = sigma(n)\n; \\ Michel Marcus, Sep 18 2015

Formula

a(n) = floor(A017665(n)/A017666(n)). - Michel Marcus, Sep 18 2015

Extensions

More terms from Robert G. Wilson v, Jun 28 2005