

A005528


Størmer numbers or arccotangent irreducible numbers: largest prime factor of n^2 + 1 is >= 2n.
(Formerly M0950)


9



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), 517528.


MATHEMATICA

Select[Range[96], FactorInteger[#^2 + 1][[1, 1]] >= 2 # &] (* JeanFrançois 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 !! (n1)
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



