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

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, 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, 4, 3, 5, 5, 4, 4, 6, 5, 5, 3, 4, 3, 4, 4, 3, 4, 2, 3, 4

Offset: 1

Author

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

Keywords

• nonn
• hard

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..99
• Hisanori Mishima, Factorizations of many number sequences
• R. G. Wilson v, Explicit factorizations

Crossrefs

Cf. A054988, A054990, A054991, A054992, A057588.

Programs

Mathematica

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}]]
PrimeOmega[#] & /@ (FoldList[Times, Prime[Range[81]]] - 1) (* Harvey P. Dale, Mar 11 2017 *)

Extensions

More terms from Robert G. Wilson v, Mar 24 2001

a(42)-a(81) from Charles R Greathouse IV, May 07 2011

a(82)-a(87) from Amiram Eldar, Oct 03 2019