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Search: id:A076605
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| A076605 |
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Largest prime divisor of n^2 - 1. |
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+0
3
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| 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, 73, 37, 73, 37, 11, 19, 79
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Also the largest prime that divides either n-1 or n+1.
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REFERENCES
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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.
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EXAMPLE
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n=11: the largest prime factor of 10 and 12 is 5, therefore a[11]=5.
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MATHEMATICA
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Table[ Last[ Table[ # [[1]]] & /@ FactorInteger[n^2 - 1]], {n, 2, 80}]
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PROGRAM
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(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])])))
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CROSSREFS
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Cf. A006530, A037464, A074399 (bisections).
Sequence in context: A166477 A124332 A165342 this_sequence A030640 A145051 A026741
Adjacent sequences: A076602 A076603 A076604 this_sequence A076606 A076607 A076608
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Oct 21 2002
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