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A174379 a(n) is the largest prime factor of (n-1)^n - n^(n-1).

%I A174379 #16 Sep 08 2022 08:45:51
%S A174379 17,19,167,162287,159463,354751,2486784401,12589253,71549927,
%T A174379 83695120256591,556123,10902870290089,25793,362561,26757560905578361,
%U A174379 6015993258685545623,55044966589,1182622403647894934149,9973660056412561,38783069052902219,4576344458074395243073
%N A174379 a(n) is the largest prime factor of (n-1)^n - n^(n-1).
%C A174379 A007925(n) = (n-1)^n - n^(n-1).
%C A174379 A007925(n) = -1 for n = 1..3, which has no prime factors, so the offset is 4.
%H A174379 Vincenzo Librandi, <a href="/A174379/b174379.txt">Table of n, a(n) for n = 4..50</a>
%e A174379 19 is a term because 4^5 - 5^4 = 399 = 19 * 21. - _Bernard Schott_, Jan 14 2019
%t A174379 Table[FactorInteger[(n - 1)^n - n^(n - 1)][[-1, 1]], {n, 4, 20}] (* _Vincenzo Librandi_, Jan 14 2019 *)
%o A174379 (PARI) a(n) = vecmax(factor((n-1)^n - n^(n-1))[,1]);
%o A174379 for (n=4, 30, print1(a(n), ", ")) \\ _Michel Marcus_, Jan 14 2019
%o A174379 (Magma) [Maximum(PrimeDivisors((n-1)^n - n^(n-1))): n in [4..25]]; // _Vincenzo Librandi_, Jan 14 2019
%Y A174379 Cf. A007925.
%K A174379 nonn
%O A174379 4,1
%A A174379 Torbjorn Alm (talm(AT)tele2.se), Mar 17 2010
%E A174379 a(4) corrected, a(22)-a(24) added, and other edits by _Jon E. Schoenfield_, Jan 13 2019