A053226 Numbers k for which sigma(k) > sigma(k+1).

4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 45, 46, 48, 50, 52, 54, 56, 58, 60, 64, 66, 68, 70, 72, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 106, 108, 110, 112, 114, 116, 117, 118, 120, 122, 124, 126, 128, 130

Offset: 1

Author

Asher Auel, Jan 06 2000

Keywords

• nonn

Comments

The asymptotic density of this sequence is 1/2 (Erdős, 1936). - Amiram Eldar, Mar 19 2021

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Paul Erdős, On a problem of Chowla and some related problems, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 32, No. 4 (1936), pp. 530-540; alternative link.

Crossrefs

Cf. A000203, A053222, A053224, A053238.

Programs

Haskell

import Data.List (findIndices)
a053226 n = a053226_list !! (n-1)
a053226_list = map (+ 1) $ findIndices (< 0) a053222_list
-- Reinhard Zumkeller, Oct 16 2011

Maple

with(numtheory): seq( `if`((sigma(i) > sigma(i+1)),i,print( )), i=1..139);

Mathematica

Select[Range[150], DivisorSigma[1, #] > DivisorSigma[1, # + 1] &] (* Carl Najafi, Aug 16 2011 *)

PARI

is(n)=sigma(n)>sigma(n+1) \\ Charles R Greathouse IV, Mar 09 2014