A082957 Numbers n such that sigma(2n) < sigma(2n+1).

1, 31, 37, 67, 73, 97, 127, 157, 199, 202, 229, 241, 247, 262, 277, 283, 307, 313, 331, 337, 346, 367, 379, 382, 397, 409, 427, 457, 472, 487, 499, 517, 547, 562, 577, 607, 619, 643, 661, 697, 727, 757, 769, 787, 823, 829, 841, 877, 892, 907, 913, 922, 937

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

Sequence in context: A097437 A156974 A215431 * A067826 A107013 A107012

Adjacent sequences: A082954 A082955 A082956 * A082958 A082959 A082960

Keyword

nonn

Author

Benoit Cloitre, May 26 2003

Status

approved