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Number of prime factors of n^n - 1, counted with multiplicity.
5

%I #19 Jul 04 2024 03:36:51

%S 1,2,3,4,4,4,7,8,6,4,8,6,5,7,7,7,10,4,11,10,8,6,13,13,11,9,13,10,15,4,

%T 13,12,13,10,18,11,8,10,16,9,16,6,15,18,9,5,19,20,14,15,17,8,16,12,18,

%U 10,10,5,26,8,10,14,20,19,17,9,17,12,19,7,29,15,8,11,20,13,21,8

%N Number of prime factors of n^n - 1, counted with multiplicity.

%H Amiram Eldar, <a href="/A309941/b309941.txt">Table of n, a(n) for n = 2..138</a> (terms 2..126 from Chai Wah Wu)

%H factordb, <a href="http://factordb.com/index.php?query=n%5En-1&amp;use=n&amp;perpage=20&amp;format=1&amp;sent=1&amp;PR=1&amp;PRP=1&amp;C=1&amp;CF=1&amp;U=1&amp;FF=1&amp;VP=1&amp;EV=1&amp;OD=1&amp;VC=1&amp;n=80">Factors of n^n-1</a>.

%e a(3) = 2: 3^3 - 1 = 26 = 2 * 13.

%e a(5) = 4: 5^5 - 1 = 3124 = 2^2 * 11 * 71.

%t a[n_] := PrimeOmega[n^n - 1]; Array[a, 45, 2] (* _Amiram Eldar_, Jul 04 2024 *)

%o (PARI) for(k=2, 50, print1(bigomega(k^k-1),", "))

%Y Cf. A006486, A048861, A085723, A116895, A125135, A334167, A344870.

%K nonn,hard

%O 2,2

%A _Hugo Pfoertner_, Aug 24 2019