OFFSET
1,2
COMMENTS
There are 2301 primes and 3169 composites among the 5470 first terms. Does limit n->infinity card(k : a(k) prime)/card(k : a(k) composite) > 0 ?
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
Mits Kobayashi, Tim Trudgian, On integers n for which sigma(2n+1)>=sigma(2n), arXiv:1904.10064 [math.NT], 2019.
Vaclav Kotesovec, Plot of a(n)/n for n = 1..50000
FORMULA
Conjecture : a(n) is asymptotic to c*n where 18<c<18.5.
MAPLE
q:= n-> (s-> s(2*n)<s(2*n+1))(numtheory[sigma]):
select(q, [$1..1000])[]; # Alois P. Heinz, Apr 24 2019
MATHEMATICA
Select[Range[1, 1000], DivisorSigma[1, 2*#] < DivisorSigma[1, 2*#+1]&] (* Vaclav Kotesovec, Feb 15 2019 *)
PROG
(PARI) isok(n) = sigma(2*n) < sigma(2*n+1); \\ Michel Marcus, Dec 04 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, May 26 2003
STATUS
approved