Greatest prime factor of n^2 - 1, n ≥ 2

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Also the greatest prime factor (i.e. the largest prime divisor) of either

n  −  1

or

n  +  1

.

Sequences

A076605 Largest prime divisor of

n 2  −  1, n   ≥   2

.

{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, 7, ...}

A175607 Largest number

x

such that the greatest prime factor of

x 2  −  1

is

pn

.

{3, 17, 161, 8749, 19601, 246401, 672281, 23718421, 10285001, 354365441, 3222617399, 9447152318, 127855050751, 842277599279, 2218993446251, 2907159732049, 41257182408961, 63774701665793, 25640240468751, ...}

See also

• {{Sequence of the Day for July 21}}