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

Author

Benoit Cloitre, May 26 2003

Keywords

• nonn

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

Programs

Maple

q:= n-> (s-> s(2*n)Alois P. Heinz, Apr 24 2019

Mathematica

Select[Range[1, 1000], DivisorSigma[1,2*#] < DivisorSigma[1,2*#+1]&] (* Vaclav Kotesovec, Feb 15 2019 *)

PARI

isok(n) = sigma(2*n) < sigma(2*n+1); \\ Michel Marcus, Dec 04 2013

Formula

Conjecture : a(n) is asymptotic to c*n where 18

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