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A076605 Largest prime divisor of n^2 - 1. 5
3, 2, 5, 3, 7, 3, 7, 5, 11, 5, 13, 7, 13, 7, 17, 3, 19, 5, 19, 11, 23, 11, 23, 13, 5, 13, 29, 7, 31, 5, 31, 17, 11, 17, 37, 19, 37, 19, 41, 7, 43, 11, 43, 23, 47, 23, 47, 5, 17, 13, 53, 13, 53, 7, 19, 29, 59, 29, 61, 31, 61, 31, 13, 11, 67, 17, 67, 17, 71, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Also the largest prime that divides either n-1 or n+1.

REFERENCES

D. H. Lehmer, "On a problem of Stormer", Illinois J. Math. 8, 1964, pp. 57 - 79.

K. Mahler, "Uber den grossten Primteiler spezieller Polynome zweiten Grades", Arch. Math. Naturvid. B.41, 1935, pp. 3 - 26.

C. Stormer "Quelques theoremes sur l'equation de Pell x^2 - D y^2 = +/-1 et leur applications", Vid. Skr. I Math. Natur. Kl.(Christiana), 1897, No. 2, 48 pp.

LINKS

T. D. Noe, Table of n, a(n) for n = 2..10000

EXAMPLE

n=11: the largest prime factor of 10 and 12 is 5, therefore a(11) = 5.

MATHEMATICA

Table[ Last[ Table[ # [[1]]] & /@ FactorInteger[n^2 - 1]], {n, 2, 80}]

PROG

(PARI) for (n=3, 100, print1(", "max(factor(n-1)[, 1][length(factor(n-1)[, 1])], factor(n+1)[, 1][length(factor(n+1)[, 1])])))

CROSSREFS

Cf. A006530, A037464, A074399 (bisections).

Cf. A175607.

Sequence in context: A124332 A246416 A165342 * A194748 A030640 A176447

Adjacent sequences:  A076602 A076603 A076604 * A076606 A076607 A076608

KEYWORD

nonn

AUTHOR

Jon Perry, Oct 21 2002

STATUS

approved

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Last modified November 27 17:39 EST 2014. Contains 250249 sequences.