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A054989 Number of prime divisors of -1 + (product of first n primes). 9

%I

%S 0,1,1,2,1,1,2,3,3,2,2,4,1,2,3,3,2,3,3,2,2,4,3,1,2,2,4,4,4,3,3,3,3,3,

%T 3,4,4,4,5,3,5,4,5,4,4,4,4,2,3,3,2,4,3,4,2,4,4,7,4,3,3,4,4,3,3,1,3,1,

%U 4,3,5,5,4,4,6,5,5,3,4,3,4,4,3,4,2,3,4

%N Number of prime divisors of -1 + (product of first n primes).

%H Amiram Eldar, <a href="/A054989/b054989.txt">Table of n, a(n) for n = 1..99</a>

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha103.htm">Factorizations of many number sequences</a>

%H R. G. Wilson v, <a href="/A038507/a038507.txt">Explicit factorizations</a>

%e a(4)=2 because 2*3*5*7 - 1 = 209 = 11*19

%t a[q_] := Module[{x, n}, x=FactorInteger[Product[Table[Prime[i], {i, q}][[j]], {j, q}]-1]; n=Length[x]; Sum[Table[x[[i]][[2]], {i, n}][[j]], {j, n}]]

%t PrimeOmega[#] & /@ (FoldList[Times, Prime[Range[81]]] - 1) (* _Harvey P. Dale_, Mar 11 2017 *)

%Y Cf. A054988, A054990, A054991, A054992.

%K nonn,hard

%O 1,4

%A Arne Ring (arne.ring(AT)epost.de), May 30 2000

%E More terms from _Robert G. Wilson v_, Mar 24 2001

%E a(42)-a(81) from _Charles R Greathouse IV_, May 07, 2011

%E a(82)-a(87) from _Amiram Eldar_, Oct 03 2019

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Last modified April 8 08:54 EDT 2020. Contains 333313 sequences. (Running on oeis4.)