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A325423 Numbers k such that sigma(2*k+1) >= sigma(2*k). 1
1, 7, 31, 37, 67, 73, 97, 103, 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, 667, 682, 697, 727, 757, 769, 787 (list; graph; refs; listen; history; text; internal format)
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
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
Cf. A082957.
Sequence in context: A241101 A238664 A272201 * A309381 A276741 A000696
KEYWORD
nonn
AUTHOR
Giuseppe Melfi, Sep 06 2019
STATUS
approved

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Last modified May 24 23:50 EDT 2024. Contains 372782 sequences. (Running on oeis4.)