OFFSET
1,2
COMMENTS
The function A(x) enumerating the terms not exceeding x has the property that lim_{x->oo} A(x)/x exists (Hildebrand, 1990).
REFERENCES
M. Laub, Advanced Problems: 6555. The American Mathematical Monthly, 94(8), 800 (1987). doi:10.2307/2323430.
LINKS
Giuseppe Melfi, Table of n, a(n) for n = 1..2763
Mits Kobayashi, Tim Trudgian, On integers n for which sigma(2n+1)>=sigma(2n), arXiv:1904.10064 [math.NT], 2019.
M. Laub & L. Mattics, Problem 6555: Odd Integers with Relatively Large Divisor Sum, The American Mathematical Monthly, 97(4), 351-353 (1990). doi:10.2307/2324532.
FORMULA
a(n) ~ c*n with 18.2 < c < 18.6 (claimed by Kobayashi and Trudgian).
EXAMPLE
7 is in the sequence because sigma(14) = 1+2+7+14 = 24 <= sigma(15) = 1+3+5+15 = 24;
31 is in the sequence because sigma(62) = 1+2+31+62 = 96 <= sigma(63) = 1+3+7+9+21+63 = 104.
MATHEMATICA
Position[Partition[DivisorSigma[1, Range[2, 1601]], 2], _?(#[[2]] >= #[[1]]&), 1, Heads->False]//Flatten (* Harvey P. Dale, Jan 10 2022 *)
PROG
(PARI) isok(n) = sigma(2*n+1) >= sigma(2*n); \\ Michel Marcus, Sep 09 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Giuseppe Melfi, Sep 06 2019
STATUS
approved