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A005528 Størmer numbers or arc-cotangent irreducible numbers: largest prime factor of n^2 + 1 is >= 2n.
(Formerly M0950)
8
1, 2, 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 39, 40, 42, 44, 45, 48, 49, 51, 52, 53, 54, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 74, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 92, 94, 95, 96 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also numbers such that n^2 + 1 has a primitive divisor, hence (by Everest & Harman, Theorem 1.4) 1.1n < a(n) < 1.88n for large enough n. They conjecture that a(n) ~ cn where c = 1/log 2 = 1.4426.... - Charles R Greathouse IV, Nov 15 2014

REFERENCES

John H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, p. 246.

Graham Everest and Glyn Harman, On primitive divisors of n^2 + b, in Number Theory and Polynomials (James McKee and Chris Smyth, ed.), London Mathematical Society 2008.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

J. Todd, Table of Arctangents. National Bureau of Standards, Washington, DC, 1951, p. 2.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Graham Everest and Glyn Harman, On primitive divisors of n^2 + b, arXiv:math/0701234 [math.NT], 2007.

J. Todd, A problem on arc tangent relations, Amer. Math. Monthly, 56 (1949), 517-528.

MATHEMATICA

Select[Range[96], FactorInteger[#^2 + 1][[-1, 1]] >= 2 # &] (* Jean-François Alcover, Apr 11 2011 *)

PROG

(PARI) is(n)=my(f=factor(n^2+1)[, 1]); f[#f]>=2*n \\ Charles R Greathouse IV, Nov 14 2014

(Haskell)

a005528 n = a005528_list !! (n-1)

a005528_list = filter (\x -> 2 * x <= a006530 (x ^ 2 + 1)) [1..]

-- Reinhard Zumkeller, Jun 12 2015

CROSSREFS

Cf. A002312, A006530.

Cf. A084925 (hyperbolic analog).

Sequence in context: A153242 A143070 A206926 * A211030 A050015 A153218

Adjacent sequences:  A005525 A005526 A005527 * A005529 A005530 A005531

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane and J. H. Conway

STATUS

approved

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Last modified August 31 19:35 EDT 2015. Contains 261251 sequences.