A053224 Numbers k for which sigma(k) < sigma(k+1).

1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 62, 63, 65, 67, 69, 71, 73, 74, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 119, 121, 123, 125, 127, 129, 131

Offset

1,2

Comments

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

Links

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

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.

Maple

with(numtheory): seq( `if`(sigma(i) < sigma(i+1), i, [][]), i=1..134);

Mathematica

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

Prog

(Haskell)
import Data.List (elemIndices)
a053224 n = a053224_list !! (n-1)
a053224_list = map (+ 1) $ elemIndices True $
   zipWith (<) a000203_list $ tail a000203_list
-- Reinhard Zumkeller, May 07 2012
(PARI) is(n)=sigma(n)<sigma(n+1) \\ Charles R Greathouse IV, Mar 09 2014

Crossrefs

Cf. A000203, A053222, A053226, A053230 (first differences).

Sequence in context: A360126 A004274 A004280 * A277334 A091377 A336119

Adjacent sequences: A053221 A053222 A053223 * A053225 A053226 A053227

Keyword

nonn

Author

Asher Auel, Jan 06 2000

Status

approved