Voozh

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

(list; graph; refs; listen; history; text; internal format)

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