A136548 a(n) = max {k >= 1 | sigma(k) <= n}.

1, 1, 2, 3, 3, 5, 5, 7, 7, 7, 7, 11, 11, 13, 13, 13, 13, 17, 17, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 29, 29, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 41, 41, 43, 43, 43, 43, 47, 47, 47, 47, 47, 47, 53, 53, 53, 53, 53, 53, 59, 59, 61, 61, 61, 61, 61, 61, 67, 67, 67, 67, 71, 71

Offset: 1

Author

Roger L. Bagula, Mar 26 2008

Keywords

• nonn
• easy

Comments

Old name was "Extended 'previous prime' version 2".

This is the same as A151799 if n >= 3 and falls back to 1, if no prime smaller than n exists.

a(n+1) is the largest number k such that A007955(k) <= n, where A007955 is the product of divisors. - Jaroslav Krizek, Apr 01 2010

For every k >= 1, the equation n - a(n) = k has infinitely many solutions. - Bernard Schott, Mar 05 2019

References

• P. Tauvel, Exercices d'Algèbre Générale et d'Arithmétique, Dunod, 2004, Exercice 18 p. 204.

Links

• Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000203 (sigma), A000142, A006530, A151799.

Programs

Mathematica

A136548[1]:= 1; A136548[2]:= 1; A136548[n_]:= Prime[PrimePi[n-1]]; Array[A136548,50] (* Enrique Pérez Herrero, Jul 23 2011 *)

Formula

a(n) = A006530(A000142(n-1)). - Michel Marcus, Jun 20 2014

For n > 1, a(n) < n. If p is prime, a(p+1) = p. - Bernard Schott, Mar 05 2019

Extensions

Definition clarified by N. J. A. Sloane, Mar 14 2019 based on a suggestion from Jaroslav Krizek, Mar 01 2010.