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%I #31 Mar 29 2023 17:41:36
%S 1,1,1,1,2,2,2,3,1,1,5,2,3,4,2,2,3,4,3,3,3,3,4,2,5,4,2,6,6,2,4,5,5,3,
%T 3,3,2,5,5,4,5,2,5,5,5,5,8,8,5,6,4,2,7,5,5,6,4,5,3,8,7,6,5,7,4,3,5,6,
%U 1,1,7,5,8,7,3,1,4,4,5,5,4,2,4,5,5,7,3,6,7,7,4,7,6,5,7,5,3,8,5,3,4,6,5,7,7
%N Number of distinct prime factors of n! + 2n - 1.
%H Sean A. Irvine, <a href="/A139465/b139465.txt">Table of n, a(n) for n = 1..118</a>
%H Florian Luca and Igor E. Shparlinski, <a href="https://doi.org/10.5802/jtnb.524">On the largest prime factor of n! + 2^n - 1</a>, Journal de Théorie des Nombres de Bordeaux 17 (2005), 859-870.
%H Apurva Rai, <a href="/A139465/a139465.py.txt">Python Program for a(81)-a(100)</a>
%H Apurva Rai, <a href="/A139465/a139465_1.py.txt">Python program for a(101)-a(105)</a>
%F a(n) = A001221(A139464(n)). - _Amiram Eldar_, Feb 05 2020
%t a = {}; Do[AppendTo[a, n! + 2 n - 1], {n, 1, 40}]; b = {}; Do[c = Length[FactorInteger[a[[n]]]]; AppendTo[b, c], {n, 1, Length[a]}]; b (* Artur Jasinski *)
%t PrimeNu @ Table[n! + 2*n - 1, {n, 1, 30}] (* _Amiram Eldar_, Feb 05 2020 *)
%o (PARI) a(n)=omega(n!+2*n-1) \\ _Charles R Greathouse IV_, Feb 01 2013
%Y Cf. A001221, A127986, A127987, A139023, A139024, A139464, A139466, A139467.
%K nonn
%O 1,5
%A _Artur Jasinski_, Apr 22 2008
%E a(41)-a(60) from _Amiram Eldar_, Feb 05 2020
%E a(61)-a(80) from _Jinyuan Wang_, Apr 03 2020
%E a(81)-a(100) from _Apurva Rai_, Sep 20 2020
%E a(101)-a(105) from _Apurva Rai_, Sep 21 2020