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%I #24 May 22 2022 19:59:18
%S 1,1,2,2,2,3,2,3,3,3,3,5,2,3,4,5,3,6,3,5,4,5,3,7,4,3,6,6,4,8,4,6,5,6,
%T 5,9,3,5,6,7,4,8,3,8,8,4,5,12,7,7,6,6,4,11,6,9,7,7,3,12,3,6,6,7,6,10,
%U 4,9,6,8,2,12,5,6,9,8,7,12,4,11,9,6,5,14,6,4,8,12,4,16,5,7,7,8,6,15,4,10,8
%N Number of distinct prime divisors of 3^n - 1.
%H <a href="/A133801/b133801.txt">Table of n, a(n) for n = 1..690</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>.
%F a(n) = omega(3^n - 1) = A001221(3^n - 1).
%e a(4) = omega(3^4 - 1) = omega(80) = omega(2^4 * 5) = 2.
%t Table[PrimeNu[3^n - 1], {n, 1, 50}] (* _G. C. Greubel_, May 21 2017 *)
%o (PARI) for(n = 1, 100, print1(omega(3^n - 1), ", "))
%Y Cf. A001221, A024023, A113913.
%K nonn
%O 1,3
%A _Ryan Propper_, Jan 06 2008
%E Terms to a(660) in b-file from _Amiram Eldar_, Feb 03 2020
%E a(661)-a(690) in b-file from _Max Alekseyev_, May 22 2022
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